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At least 1,117 records · Page 62
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Molecular basis of synaptic specificity by immunoglobulin superfamily receptors in Drosophila

In stereotyped neuronal networks, synaptic connectivity is dictated by cell surface proteins, which assign unique identities to neurons, and physically mediate axon guidance and synapse targeting. We recently identified two groups of immunoglobulin superfamily proteins in Drosophila, Dprs and DIPs, as strong candidates for synapse targeting functions. Here, we uncover the molecular basis of specificity in Dpr–DIP mediated cellular adhesions and neuronal connectivity. First, we present five crystal structures of Dpr–DIP and DIP–DIP complexes, highlighting the evolutionary and structural origins of diversification in Dpr and DIP proteins and their interactions. We further show that structures can be used to rationally engineer receptors with novel specificities or modified affinities, which can be used to study specific circuits that require Dpr–DIP interactions to help establish connectivity. We investigate one pair, engineered Dpr10 and DIP-α, for function in the neuromuscular circuit in flies, and reveal roles for homophilic and heterophilic binding in wiring.

Life Sciences & Biomedicine - Other Topics↗
DOE OSTI2012

Predictive Capability for Strongly Correlated Systems

Diffusion Monte Carlo methods can give highly accurate results for correlated systems, provided that well optimized trial wave functions with accurate nodal surfaces are employed. The Cornell team developed powerful methods for optimizing all the parameters within a multi-determinant Slater-Jastrow form of the wave function. These include the Jastrow parameters within a flexible electron-electron-nucleus form of the Jastrow function, the parameters multiplying the configuration state functions, the orbital parameters and the basis exponents. The method optimizes a linear combination of the energy and the variance of the local energy. The optimal parameters are found iteratively by diagonalizing the Hamiltonian matrix in the space spanned by the wave function and its first-order derivatives, making use of a strong zero-variance principle. It is highly robust, has become the method of choice for correlated wave function optimization and has been adopted by other QMC groups. This optimization method was used on the first-row atoms and homonuclear diatomic molecules, demonstrating that molecular well depths can be obtained with near chemical accuracy quite systematically at the diffusion Monte Carlo level for these systems. In addition the complete ground-state potential energy curve of the C 2 molecule up to the dissociation limit was obtained, and, size consistency and broken spin-symmetry issues in quantum Monte Carlo calculations were studied. The method was used with a eight-electrons-in-eight-orbitals complete active space CAS(8,8) wave function to study the relative energies of the monocyclic and bicyclic forms of m-benzyne. The DMC calculations show that the monocyclic structure is lower in energy than the bicyclic structure by 1.92 kcal/ mole, which is in excellent agreement with the best coupled cluster results (CCSD(T)) and in disagreement with the CCSD results. QMC methods have for the most part been used only for ground states of a given symmetry. We developed a method for calculating low-lying excited states as well and tested it on the ground and lowest three adiabatic excited states of methylene with progressively larger JastrowSlater multideterminant complete active space CAS wave functions. The highest of these states has the same symmetry, 1 A 1 , as the first excited state. The DMC excitation energies obtained using any of the CAS wave functions are in excellent agreement with experiment. In contrast, single-determinant wave functions do not yield accurate DMC energies, indicating that it is important to include in the wave function Slater determinants that describe static strong correlation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Triplet Tuning: A Novel Family of Non-Empirical Exchange–Correlation Functionals

In the framework of density functional theory (DFT), the lowest triplet excited state (T1) can be evaluated using multiple formulations, the most straightforward of which are unrestricted density functional theory (UDFT) and time-dependent density functional theory (TDDFT). Assuming the exact exchange-correlation (XC) functional is applied, UDFT and TDDFT provide identical energies for T1 ( ET), which is also a constraint that we require our XC functionals to obey. However, this condition is not satisfied by most of the popular XC functionals, leading to inaccurate predictions of low-lying, spectroscopically and photochemically important excited states, such as T1 and the lowest singlet excited state (S1). Inspired by the optimal tuning strategy for frontier orbital energies [T. Stein, L. Kronik, and R. Baer, J. Am. Chem. Soc. 2009, 131, 2818], we proposed a novel and nonempirical prescription of constructing an XC functional in which the agreement between UDFT and TDDFT in ET is strictly enforced. Referred to as "triplet tuning", our procedure allows us to formulate the XC functional on a case-by-case basis, using the molecular structure as the exclusive input, without fitting to any experimental data. The first triplet tuned XC functional, TT-ωPBEh, is formulated as a long-range-corrected (LRC) hybrid of Perdew-Burke-Ernzerhof (PBE) and Hartree-Fock (HF) functionals [M. A. Rohrdanz, K. M. Martins, and J. M. Herbert, J. Chem. Phys. 2009, 130, 054112] and tested on four sets of large organic molecules. Compared to existing functionals, TT-ωPBEh manages to provide more accurate predictions for key spectroscopic and photochemical observables, including but not limited to ET, the optical band gap ( ES), the singlet-triplet gap (Δ EST), and the vertical ionization potential ( I⊥), as it adjusts the effective electron-hole interactions to arrive at the correct excitation energies. This promising triplet tuning scheme can be applied to a broad range of systems that were notorious in DFT for being extremely challenging.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Third-Order Møller–Plesset Theory Made More Useful? The Role of Density Functional Theory Orbitals

The practical utility of Møller–Plesset (MP) perturbation theory is severely constrained by the use of Hartree–Fock (HF) orbitals. It has recently been shown that the use of regularized orbital-optimized MP2 orbitals and scaling of MP3 energy could lead to a significant reduction in MP3 error. In this work, we examine whether density functional theory (DFT)-optimized orbitals can be similarly employed to improve the performance of MP theory at both the MP2 and MP3 levels. We find that the use of DFT orbitals leads to significantly improved performance for prediction of thermochemistry, barrier heights, noncovalent interactions, and dipole moments relative to the standard HF-based MP theory. Indeed, MP3 (with or without scaling) with DFT orbitals is found to surpass the accuracy of coupled-cluster singles and doubles (CCSD) for several data sets. We also found that the results are not particularly functional sensitive in most cases (although range-separated hybrid functionals with low delocalization error perform the best). As such, MP3 based on DFT orbitals thus appears to be an efficient, noniterative O(N 6 ) scaling wave-function approach for single-reference electronic structure computations. Scaled MP2 with DFT orbitals is also found to be quite accurate in many cases, although modern double hybrid functionals are likely to be considerably more accurate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Push it to the limit: comparing periodic and local approaches to density functional theory for intermolecular interactions

With the aim of systematically comparing two popular approaches to density functional theory–all-electron calculations with local basis sets, and periodic calculations employing plane wave basis sets and norm-conserving pseudopotentials–we have computed complete-basis binding energies across the S22 set of intermolecular interactions, a dataset consisting of noncovalent interactions of small- and medium-sized molecules containing first- and second-row atoms, using the Troullier-Martins norm-conserving pseudopotentials with SPW92, a local spin-density approximation; and PBE, a generalised gradient approximation. Here, we have found that it is challenging to reach the basis set limit with these periodic calculations; for the methods and systems examined, a minimum vacuum distance of 30 Å between a system and its nearest images is necessary–unless some form of dipole correction is employed–as is a kinetic energy cutoff of at least 80 Ry. The trends in convergence with respect to vacuum size and kinetic energy cutoff are largely independent of the level of density functional approximation employed. A sense of the impact of each hyperparameter on basis set error provides a foundation for ensuring quality calculations in future studies and allows us to quantify the basis set errors incurred in existing studies on similar systems.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Giant Dipole Moments: Remarkable Effects Mono‐, Di‐, and Tri‐ Hydrated 5,6‐Diaminobenzene‐1,2,3,4‐Tetracarbonnitrile

The molecule 5,6-diaminobenzene-1,2,3,4-tetracarbonnitrile (MOI) was first synthesized by Müllen and coworkers in 2016 and boasts an ultrastrong dipole moment of $14.1\pm 0.7$ Debye in THF. Gas phase DFT computations do not fully reflect this ultrastrong dipole moment, demonstrating the role of solvent in increasing this dipole moment. Here, we investigate the effect of solvent molecule position on the dipole moment of this species, computationally examining systems with giant dipole moments. These systems are optimized in the gas phase with the B3LYP functional, employing the aug-cc-pVTZ and def2-TZVP basis sets, as well as the B3LYP-D3BJ/aug-cc-pVTZ functional in Orca. Single point DLPNO-CCSD/aug-cc-pVDZ results were obtained from Orca and Psi4, as well as DLPNO-CCSD(T)/CBS information from Psi4. Additionally, these are compared to the dipole moments of di- and tri-hydrated systems, and the SMD models for THF and water at the B3LYP/aug-cc-pVTZ level of theory. The dissociation energies, HOMO-LUMO energy gaps, and dipole moments are presented. These metrics show the nh1nh1′ THF system boasts the largest dissociation energy and dipole moment of the singly solvated systems, due to its strong hydrogen bonding. The importance of solvent placement is highlighted and may guide the synthesis of macromolecules or organic frameworks incorporating the MOI or MOI-like subunits. Remarkably, a single solvent molecule provides a good model for the difference between the gas phase and solvated species. The predicted gas phase dipole moments computed with B3LYP/aug-cc-pVTZ for the MOI, its monohydrated complex, dihydrated complex, and its trihydrated complex are 9.6, 14.2, 16.0, and 16.8 Debye, respectively.

dipole↗
DOE OSTI2016

Note: The performance of new density functionals for a recent blind test of non-covalent interactions

Benchmark datasets of non-covalent interactions are essential for assessing the performance of density functionals and other quantum chemistry approaches. In a recent blind test, Taylor et al. benchmarked 14 methods on a new dataset consisting of 10 dimer potential energy curves calculated using coupled cluster with singles, doubles, and perturbative triples (CCSD(T)) at the complete basis set (CBS) limit (80 data points in total). Finally, the dataset is particularly interesting because compressed, near-equilibrium, and stretched regions of the potential energy surface are extensively sampled.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

Structure of human dual-specificity phosphatase 27 at 2.38 Å resolution

There are over 100 genes in the human genome that encode protein tyrosine phosphatases (PTPs) and approximately 60 of these are classified as dual-specificity phosphatases (DUSPs). Although many dual-specificity phosphatases are still not well characterized, novel functions have been discovered for some of them that have led to new insights into a variety of biological processes and the molecular basis for certain diseases. Indeed, as the functions of DUSPs continue to be elucidated, a growing number of them are emerging as potential therapeutic targets for diseases such as cancer, diabetes and inflammatory disorders. Here, the overexpression, purification and structure determination of DUSP27 at 2.38 {angstrom} resolution are presented.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2018

3-[4-Bromo-α(R*)-methoxybenzyl]-6-chloro-3(S*),4(S*)-dihydroxychroman: X-ray and DFT Studies

Sodium borohydride reduction of E-3-benzylidenechromanone epoxides in dry methanol has afforded 3(S*), 4(S*)-dihydroxy-3-[α(R*)-methoxybenzyl]chromans as an interesting class of products, the structures of which have been assigned mainly from spectral data and consideration of the mechanistic aspects. X-ray diffraction study of one of them, 3-[4-bromo-α(R*)-methoxybenzyl]-6-chloro-3(S*),4(S*)- dihydroxychroman, is performed. The title compound crystallizes in the monoclinic sp. gr. P2{sub 1}/n, with a = 13.336(6) Å, b = 10.866(5) Å, c = 27.166(11) Å, β = 95.193(6)°, V = 3920(3) Å{sup 3}, and Z = 8. Supramolecular construction of the compound involves O–H···O intermolecular hydrogen bonds as well as three other types of non-covalent interactions which are responsible for crystal packing. Density functional theory was applied for geometry optimization, molecular orbital calculations, and prediction of UV spectral features. The geometric parameters (bond lengths, bond angles, and dihedral angles) for the representative compound obtained from density functional theory with B3LY6-31G basis set were in good agreement with experimental values.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Non-additive non-interacting kinetic energy of rare gas dimers

We show approximations of the non-additive non-interacting kinetic energy (NAKE) as an explicit functional of the density are the basis of several electronic structure methods that provide improved computational efficiency over standard Kohn-Sham calculations. However, within most fragment-based formalisms, there is no unique exact NAKE, making it difficult to develop general, robust approximations for it. When adjustments are made to the embedding formalisms to guarantee uniqueness, approximate functionals may be more meaningfully compared to the exact unique NAKE. We use numerically accurate inversions to study the exact NAKE of several rare-gas dimers within partition density functional theory, a method that provides the uniqueness for the exact NAKE. We find that the NAKE decreases nearly exponentially with atomic separation for the rare-gas dimers. We compute the logarithmic derivative of the NAKE with respect to the bond length for our numerically accurate inversions as well as for several approximate NAKE functionals. We show that standard approximate NAKE functionals do not reproduce the correct behavior for this logarithmic derivative and propose two new NAKE functionals that do. The first of these is based on a re-parametrization of a conjoint Perdew-Burke-Ernzerhof (PBE) functional. The second is a simple, physically motivated non-decomposable NAKE functional that matches the asymptotic decay constant without fitting.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Comprehensive Basis-Set Testing of Extended Symmetry-Adapted Perturbation Theory and Assessment of Mixed-Basis Combinations to Reduce Cost

Hybrid or “extended” symmetry-adapted perturbation theory (XSAPT) replaces traditional SAPT’s treatment of dispersion with better performing alternatives while at the same time extending two-body (dimer) SAPT to a many-body treatment of polarization using a self-consistent charge embedding procedure. The present work presents a systematic study of how XSAPT interaction energies and energy components converge with respect to the choice of Gaussian basis set. Errors can be reduced in a systematic way using correlation-consistent basis sets, with aug-cc-pVTZ results converged within <0.1 kcal/mol. Similar (if slightly less systematic) behavior is obtained using Karlsruhe basis sets at much lower cost, and we introduce new versions with limited augmentation that are even more efficient. Pople-style basis sets, which are more efficient still, often afford good results if a large number of polarization functions are included. The dispersion models used in XSAPT afford much faster basis-set convergence as compared to the perturbative description of dispersion in conventional SAPT, meaning that “compromise” basis sets (such as jun-cc-pVDZ) are no longer required and benchmark-quality results can be obtained using triple-ζ basis sets. The use of diffuse functions proves to be essential, especially for the description of hydrogen bonds. As a result, the “δ(Hartree–Fock)” correction for high-order induction can be performed in double-ζ basis sets without significant loss of accuracy, leading to a mixed-basis approach that offers 4× speedup over the existing (cubic scaling) XSAPT approach.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2018

Compressive Deformation Behavior of Open-Cell Cu-Zn-Al Alloy Foam Made Through P/M Route Using Mechanically Alloyed Powder

Cu-Zn-Al foams of varying porosity fractions using mechanical alloyed powder have been made through powder metallurgy route. Here, NH{sub 4} (HCO{sub 3}) was used as a space holder. Mechanically alloyed Cu-Zn-Al is made using a planetary ball mill taking the ratio of Cu/Zn/Al = 70:25:5 (by weight ratio). The ball/powder ratios were varied in the four ranges 10:1, 15:1, 20:1, and 25:1. Green compacts of milled powder and space holder samples were sintered at three stages at three different temperatures 350, 550, and 850 °C for 1 h at each stage. The crystalline size and particle size as a function of ball/powder ratios were examined. The compressive deformation responses of foams are varied with relative density and the ball/powder ratio. The plateau stress and energy absorption of these foams increase with an increase in relative density but decreases with increase in ball/powder ratio, even though crystalline size decreases. This has further been explained on the basis of particle morphology as a function of ball/powder ratio.

36 MATERIALS SCIENCE↗
DOE OSTI2017

On extending Kohn-Sham density functionals to systems with fractional number of electrons

Here, we analyze four ways of formulating the Kohn-Sham (KS) density functionals with a fractional number of electrons, through extending the constrained search space from the Kohn-Sham and the generalized Kohn-Sham (GKS) non-interacting $\mathcal{v}$-representable density domain for integer systems to four different sets of densities for fractional systems. In particular, these density sets are (I) ensemble interacting N -representable densities, (II) ensemble non-interacting N -representable densities, (III) non-interacting densities by the Janak construction, and (IV) non-interacting densities whose composing orbitals satisfy the Aufbau occupation principle. By proving the equivalence of the underlying first order reduced density matrices associated with these densities, we show that sets (I), (II), and (III) are equivalent, and all reduce to the Janak construction. Moreover, for functionals with the ensemble v-representable assumption at the minimizer, (III) reduces to (IV) and thus justifies the previous use of the Aufbau protocol within the (G)KS framework in the study of the ground state of fractional electron systems, as defined in the grand canonical ensemble at zero temperature. By further analyzing the Aufbau solution for different density functional approximations (DFAs) in the (G)KS scheme, we rigorously prove that there can be one and only one fractional occupation for the Hartree Fock functional, while there can be multiple fractional occupations for general DFAs in the presence of degeneracy. This has been confirmed by numerical calculations using the local density approximation as a representative of general DFAs. This work thus clarifies important issues on density functional theory calculations for fractional electron systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Robust, Accurate, and Efficient: Quantum Embedding Using the Huzinaga Level-Shift Projection Operator for Complex Systems

Using wave function (WF) in density functional theory (DFT) embedding methods provides a framework for performing localized, high-accuracy WF calculations on a system, while not incurring the full computational cost of the WF calculation on the full system. To effectively partition a system into localized WF and DFT subsystems, we utilize the Huzinaga level-shift projection operator within an absolutely localized basis. In this work, we study the ability of the absolutely localized Huzinaga level-shift projection operator method to study complex WF and DFT partitions, including partitions between multiple covalent bonds, a double bond, and transition-metal–ligand bonds. We find that our methodology can accurately describe all of these complex partitions. Additionally, we study the robustness of this method with respect to the WF method, specifically where the embedded systems were described using a multiconfigurational WF method. We found that the method is systematically improvable with respect to both the number of atoms in the WF region and the size of the basis set used, with energy errors less than 1 kcal/mol. Additionally, we calculated the adsorption energy of H2 to a model of an iron metal–organic framework (Fe-MOF-74) to within 1 kcal/mol compared to CASPT2 calculations performed on the full model while incurring only a small fraction of the full computational cost. In conclusion, this work demonstrates that the absolutely localized Huzinaga level-shift projection operator method is applicable to very complex systems with difficult electronic structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Functional genomics of the rapidly replicating bacterium Vibrio natriegens by CRISPRi

We present that the fast-growing Gram-negative bacterium Vibrio natriegens is an attractive microbial system for molecular biology and biotechnology due to its remarkably short generation time and metabolic prowess. However, efforts to uncover and utilize the mechanisms underlying its rapid growth are hampered by the scarcity of functional genomic data. Here, we develop a pooled genome-wide clustered regularly interspaced short palindromic repeats (CRISPR) interference (CRISPRi) screen to identify a minimal set of genes required for rapid wild-type growth. Targeting 4,565 (99.7%) of predicted protein-coding genes, our screen uncovered core genes comprising putative essential and growth-supporting genes that are enriched for respiratory pathways. We found that 96% of core genes were located on the larger chromosome 1, with growth-neutral duplicates of core genes located primarily on chromosome 2. Lastly, our screen also refines metabolic pathway annotations by distinguishing functional biosynthetic enzymes from those predicted on the basis of comparative genomics. Taken together, this work provides a broadly applicable platform for high-throughput functional genomics to accelerate biological studies and engineering of V. natriegens.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2013

Reconstruction of Long-Lived Radionuclide Intakes for Techa Riverside Residents: Cesium-137

Radioactive contamination of the Techa River (Southern Urals, Russia) occurred from 1949–1956 due to routine and accidental releases of liquid radioactive wastes from the Mayak Production Association. The long-lived radionuclides in the releases were 90Sr and 137Cs. Contamination of the components of the Techa River system resulted in chronic external and internal exposure of about 30,000 residents of riverside villages. Data on radionuclide intake with diet are used to estimate internal dose in the Techa River Dosimetry System (TRDS), which was elaborated for the assessment of radiogenic risk for Techa Riverside residents. The 90Sri ntake function was recently improved taking into account the recently available archival data on radionuclide releases and in-depth analysis of the extensive data on 90Sr measurements in Techa Riverside residents. The main purpose of this paper is to evaluate the dietary intake of 137Cs by Techa Riverside residents. The 137Cs intake with river water used for drinking was reconstructed on the basis of the 90Sr intake-function and the concentration ratio 137Cs/90Sr in river water. Intake via 137Cs transfer from floodplain soil to grass and cows’ milk was evaluated for the first time. As a result, the maximal 137Cs intake level was indicated near the site of releases in upper-Techa River settlements (8,000–9,000 kBq). For villages located on the lower Techa River the 137Cs intake was significantly less (down to 300 kBq). Cows’ milk was the main source of 137Cs in diet in the upper-Techa.

cesium-137↗
DOE OSTI2011

First-principles study of boron oxygen hole centers in crystals: Electronic structures and nuclear hyperfine and quadrupole parameters

The electronic structures, nuclear hyperfine coupling constants, and nuclear quadrupole parameters of fundamental boron oxygen hole centers (BOHCs) in zircon (ZrSiO{sub 4}, I4{sub 1}/amd) and calcite (CaCO{sub 3}, R3c) have been investigated using ab initio Hartree-Fock (HF) and various density functional theory (DFT) methods based on the supercell models with all-electron localized basis sets. Both exact HF exchange and appropriate correlation functionals are important in describing the BOHCs, and the parameter-free hybrid method based on Perdew, Burke, and Ernzerhof density functionals (PBE0) turns out to be the best DFT method in reproducing the electron paramagnetic resonance (EPR) data. Our results reveal three distinct types of simple-spin (S = 1/2) [BO{sub 3}]{sup 2-} centers in calcite: (i) the classic [BO{sub 3}]{sup 2-} radical with the D{sub 3h} symmetry and the unpaired spin equally distributed on the three oxygen atoms (i.e. the O{sub 3}{sup 5-} type); (ii) the previously reported [BO{sub 2}]{sup 0} center with the unpaired spin equally distributed on two of the three oxygen atoms (O{sub 2}{sup 3-}); and (iii) a new variety with {approx}90% of its unpaired spin localized on one (O{sup -}) of the three oxygen atoms with a long B-O bond (1.44 A). Calculations confirm the unusual [BO{sub 4}]{sup 0} center in zircon and show it to arise from a highly distorted configuration with 90% of the unpaired spin on one oxygen atom that has a considerably longer B-O bond (1.68 A) than its three counterparts (1.45 A). The calculated magnitudes and directions of {sup 11}B and {sup 17}O hyperfine coupling constants and nuclear quadrupole constants for the [BO{sub 4}]{sup 0} center in zircon are in excellent agreement with the 15 K EPR experimental data. These BOHCs are all characterized by a small negative spin density on the central B atom arising from spin polarization. Our calculations also demonstrate that the spin densities on BOHCs are affected substantially by crystalline environments, and so periodic boundary treatment, such as the supercell scheme, is a must in accounting for the electronic and spin structures of BOHCs in crystals. These atomistic and electronic models of BOHCs in the crystalline matrices provide new insights into their precursors and counterparts in glasses and other amorphous materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Discretising the velocity distribution for directional dark matter experiments

Dark matter (DM) direct detection experiments which are directionally-sensitive may be the only method of probing the full velocity distribution function (VDF) of the Galactic DM halo. We present an angular basis for the DM VDF which can be used to parametrise the distribution in order to mitigate astrophysical uncertainties in future directional experiments and extract information about the DM halo. This basis consists of discretising the VDF in a series of angular bins, with the VDF being only a function of the DM speed v within each bin. In contrast to other methods, such as spherical harmonic expansions, the use of this basis allows us to guarantee that the resulting VDF is everywhere positive and therefore physical. We present a recipe for calculating the event rates corresponding to the discrete VDF for an arbitrary number of angular bins N and investigate the discretisation error which is introduced in this way. For smooth, Standard Halo Model-like distribution functions, only N=3 angular bins are required to achieve an accuracy of around 10–30% in the number of events in each bin. Shortly after confirmation of the DM origin of the signal with around 50 events, this accuracy should be sufficient to allow the discretised velocity distribution to be employed reliably. For more extreme VDFs (such as streams), the discretisation error is typically much larger, but can be improved with increasing N. This method paves the way towards an astrophysics-independent analysis framework for the directional detection of dark matter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗