diff --git a/joss.06864/10.21105.joss.06864.crossref.xml b/joss.06864/10.21105.joss.06864.crossref.xml new file mode 100644 index 0000000000..588e39c108 --- /dev/null +++ b/joss.06864/10.21105.joss.06864.crossref.xml @@ -0,0 +1,796 @@ + + + + 20240723133434-9c18d829c430a5aa261b32bda13053ba6f0e6a3a + 20240723133434 + + JOSS Admin + admin@theoj.org + + The Open Journal + + + + + Journal of Open Source Software + JOSS + 2475-9066 + + 10.21105/joss + https://joss.theoj.org + + + + + 07 + 2024 + + + 9 + + 99 + + + + VOTCA: multiscale frameworks for quantum and classical +simulations in soft matter + + + + Björn + Baumeier + https://orcid.org/0000-0002-6077-0467 + + + Jens + Wehner + https://orcid.org/0000-0003-1203-5000 + + + Nicolas + Renaud + https://orcid.org/0000-0001-9589-2694 + + + Felipe Zapata + Ruiz + https://orcid.org/0000-0001-8286-677X + + + Rene + Halver + https://orcid.org/0000-0002-4895-3762 + + + Pranav + Madhikar + https://orcid.org/0000-0003-3658-3685 + + + Ruben + Gerritsen + https://orcid.org/0000-0003-0738-8952 + + + Gianluca + Tirimbo + https://orcid.org/0000-0002-6641-0761 + + + Javier + Sijen + + + David + Rosenberger + https://orcid.org/0000-0001-6620-6499 + + + Joshua S. + Brown + https://orcid.org/0000-0003-1227-6429 + + + Vivek + Sundaram + https://orcid.org/0000-0002-9986-8461 + + + Jakub + Krajniak + https://orcid.org/0000-0001-9372-6975 + + + Marvin + Bernhardt + https://orcid.org/0000-0001-6520-5208 + + + Christoph + Junghans + https://orcid.org/0000-0003-0925-1458 + + + + 07 + 23 + 2024 + + + 6864 + + + 10.21105/joss.06864 + + + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + http://creativecommons.org/licenses/by/4.0/ + + + + Software archive + 10.5281/zenodo.12750697 + + + GitHub review issue + https://github.com/openjournals/joss-reviews/issues/6864 + + + + 10.21105/joss.06864 + https://joss.theoj.org/papers/10.21105/joss.06864 + + + https://joss.theoj.org/papers/10.21105/joss.06864.pdf + + + + + + Recent developments in the PySCF program +package + Sun + The Journal of Chemical +Physics + 2 + 153 + 10.1063/5.0006074 + 0021-9606 + 2020 + Sun, Q., Zhang, X., Banerjee, S., +Bao, P., Barbry, M., Blunt, N. 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The European Physical +Journal Special Topics, 227, 1789–1816. +https://doi.org/10.1140/epjst/e2019-800186-9 + + + + + + diff --git a/joss.06864/10.21105.joss.06864.pdf b/joss.06864/10.21105.joss.06864.pdf new file mode 100644 index 0000000000..ebcd9e425e Binary files /dev/null and b/joss.06864/10.21105.joss.06864.pdf differ diff --git a/joss.06864/paper.jats/10.21105.joss.06864.jats b/joss.06864/paper.jats/10.21105.joss.06864.jats new file mode 100644 index 0000000000..6e7b336f54 --- /dev/null +++ b/joss.06864/paper.jats/10.21105.joss.06864.jats @@ -0,0 +1,1895 @@ + + +
+ + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +6864 +10.21105/joss.06864 + +VOTCA: multiscale frameworks for quantum and classical +simulations in soft matter + + + +https://orcid.org/0000-0002-6077-0467 + +Baumeier +Björn + + + +* + + +https://orcid.org/0000-0003-1203-5000 + +Wehner +Jens + + + + + + +https://orcid.org/0000-0001-9589-2694 + +Renaud +Nicolas + + + + +https://orcid.org/0000-0001-8286-677X + +Ruiz +Felipe Zapata + + + + +https://orcid.org/0000-0002-4895-3762 + +Halver +Rene + + + + +https://orcid.org/0000-0003-3658-3685 + +Madhikar +Pranav + + + + + +https://orcid.org/0000-0003-0738-8952 + +Gerritsen +Ruben + + + + + +https://orcid.org/0000-0002-6641-0761 + +Tirimbo +Gianluca + + + + + + +Sijen +Javier + + + + + +https://orcid.org/0000-0001-6620-6499 + +Rosenberger +David + + + + +https://orcid.org/0000-0003-1227-6429 + +Brown +Joshua S. + + + + +https://orcid.org/0000-0002-9986-8461 + +Sundaram +Vivek + + + + + +https://orcid.org/0000-0001-9372-6975 + +Krajniak +Jakub + + + + +https://orcid.org/0000-0001-6520-5208 + +Bernhardt +Marvin + + + + +https://orcid.org/0000-0003-0925-1458 + +Junghans +Christoph + + +* + + + +Department of Mathematics and Computer Science, Eindhoven +University of Technology, the Netherlands + + + + +Institute for Complex Molecular Systems, Eindhoven +University of Technology, the Netherlands + + + + +Netherlands eScience Center, the Netherlands + + + + +Forschungszentrum Jülich, Jülich, Germany + + + + +Freie Universität Berlin, Berlin, Germany + + + + +Oak Ridge National Laboratory, Oak Ridge, TN, +USA + + + + +Independent researcher, Poznań, Poland + + + + +Technische Universität Darmstadt, Darmstadt, +Germany + + + + +Los Alamos National Laboratory, Los Alamos, New Mexico, +USA + + + + +* E-mail: +* E-mail: + + +10 +5 +2024 + +9 +99 +6864 + +Authors of papers retain copyright and release the +work under a Creative Commons Attribution 4.0 International License (CC +BY 4.0) +2022 +The article authors + +Authors of papers retain copyright and release the work under +a Creative Commons Attribution 4.0 International License (CC BY +4.0) + + + +coarse-graining +DFT +Quantum calculations + + + + + + Summary +

Many physical phenomena in liquids and soft matter are multiscale + by nature and can involve processes with quantum and classical degrees + of freedom occurring over a vast range of length- and timescales. + Examples range from structure formation processes of complex polymers + or even polymer blends + (Svaneborg + & Everaers, 2023) on the classical side to charge and + energy transport and conversion processes + (Lee et + al., 2019) involving explicit electronic and, therefore, + quantum information.

+

The Versatile Object-oriented Toolkit for Coarse-graining + Applications (VOTCA) provides multiscale frameworks built on a + comprehensive set of methods for the development of classical + coarse-grained potentials (VOTCA-CSG) as well as state-of-the art + excited state electronic structure methods based on density-functional + and many-body Green’s function theories, coupled in mixed + quantum-classical models and used in kinetic network models + (VOTCA-XTP).

+ +

Overview of the different VOTCA modules and external + interfaces. The trajectory reader of VOTCA-CSG in the dashed line + box are reused by + VOTCA-XTP.

+ +
+
+ + Statement of need +

VOTCA was originally developed as a platform for development and + comparison of coarse-graining (CSG) methods. Since the last software + publication in 2015, VOTCA-CSG was strengthened by adding more + methods, more examples, and involving more developers. Many users have + used VOTCA to compare different coarse-graining strategies on a + neutral ground and, if needed, proceeded with a more specialized + package based on the gained insight + (Rudzinski + et al., 2021). Such other coarse-graining packages include, + among others, BOCS + (Dunn et + al., 2018), DeePCG + (Zhang + et al., 2018), IBIsCO + (Karimi-Varzaneh + et al., 2011), MagiC + (Mirzoev + & Lyubartsev, 2013) and OpenMSCG + (Peng + et al., 2023), some of which are not open-source or specialized + in one method. Others are no longer being maintained or lack + contributions from the greater community. It is difficult to build an + all-inclusive community package for coarse-graining as it is sometimes + hard to consolidate different development styles and constantly + changing priorities from sponsors that leave little time for good + software engineering practices. In this context we would like to point + out that there is a fork of the VOTCA package + (Andrienko + et al., 2023) that contains some feature, e.g., kernel-based + machine learning methods + (Scherer + et al., 2020), that has not been merged.

+

Next to strengthening the coarse-graining functionality of VOTCA, + another major development direction taken since 2015 is the addition + of explicit quantum-mechanical modules aiming at the simulation of + static and dynamic properties of electronically excited states in + complex molecular environments using multiscale frameworks. + Specifically, the VOTCA-XTP part provides an open-source + implementation of many-body Green’s functions methods (known as + + + GW-BSE) + with the capability of linking this quantum-mechanical description of + a molecular system to a classical (microelectrostatic) environment + model, and to perform rate-based dynamic simulations with kinetic + Monte-Carlo. Basic + + GW-BSE + functionality in molecular settings has also more recently been + supported in other packages, such as Turbomole + (Balasubramani + et al., 2020), ADF + (Velde + et al., 2001), PySCF + (Sun et + al., 2020), or MOLGW + (Bruneval + et al., 2016), but these are either commercial or do not + provide links to a multiscale framework for complex environments and + dynamics.

+ + Coarse-Graining +

In the coarse-graining part of VOTCA, VOTCA-CSG, we made a lot of + improvements to the inverse Monte Carlo (IMC) method and have added + a new iterative approach, the so-called iterative integral equation + (IIE) method, which are both described in detail below and in + reference therein.

+ + Inverse Monte Carlo updates +

The inverse Monte Carlo Method introduced by Lyubartsev & + Laaksonen + (1995) + is a structure-based coarse graining method, whose goal it is to + find an effective pair potential between particles, which + reproduces the radial distribution function (RDF) of a reference + system (ref) at the coarse grained (CG) resolution. IMC has been + part of VOTCA since its first release. In the original + implementation the pair potential was determined by iteratively + solving a set of linear equations: + + + (ATA)ΔUij=AT(gijn1gijref), + where + + gij + is the RDF between particles + + i + and + + j, + + + n + indicates the iteration counter, + + ΔUij + is the potential update term, and + + A + and + + AT + are the Jacobian and its corresponding transpose. The Jacobian + + + A + is defined as: + + + A=gijUij, + where + + Uij + is the pair potential between particles i and j.

+

Rosenberger et al. + (2016), + among others + (Lyubartsev + et al., 2010; + Murtola + et al., 2007; + Tóth, + 2003), demonstrated that the standard IMC method can suffer + from numerical instabilities and/or slow convergence. Therefore, a + Tikhonov regularization + (Engl + & Ramlau, 2015) for IMC has been implemented in VOTCA. + This regularization changes the linear equations according to + Rosenberger et al. + (2016): + + + (ATA+λI)ΔUij=AT(gijn1gijref), + where + + λ + determines the strength of the regularization and + + + I + is the identity matrix. One can perform a singular value + decomposition of the Jacobian + + A + to determine an initial value for + + λ + (Rosenberger + et al., 2016). As a rule of thumb + + + λ + should at least be at the order of the smallest singular values + squared.

+
+ + Iterative Integral Equation method +

The iterative integral equation methods are similar to IMC in + that they also aim at reconstructing the RDF of a fine-grained + reference system with an effective pair potential. The main + difference is in the construction of the Jacobian, which is + approximated in IIE methods from integral equation theory + (Delbary + et al., 2020). For a molecular fluid, where each molecule + is mapped to a single bead, using the Ornstein-Zernicke equation + and the hypernetted-chain closure, one arrives at the Jacobian + inverse with the form of + + + A1=dUdg=1β(11g1(1(1+ρĥ)2)). + Here, + + ĥ + is the Fourier transform of + + h=g1 + and + + + is the Fourier operator. This approximate Jacobian works well for + systems with single-bead molecule representations with convergence + as fast as IMC, whereas in the general case, convergence is half + as fast as IMC + (Bernhardt + et al., 2023). The costly sampling of the IMC matrix is not + needed, only an RDF which is calculated on twice the range as the + potential + (Bernhardt + et al., 2021).

+
+ + Constraints +

When using the IMC or IIE methods described above to find pair + potentials, that best reproduce a reference RDF, one can use the + Gauss-Newton algorithm and formulate the problem of finding a + potential update + + ΔU + as a minimization + + where + + Δg=ggtarget. + In that case, additional constraints can be introduced. For + example, it is possible to describe the pressure of a system in + terms of the RDF + + g + and the pair potential + + U. + From a target pressure and the current pressure at each iteration, + a constraint of the form + + BΔU=d + can be described and the constraint is enforced by elimination + (Bernhardt + et al., 2021).

+
+
+ + Electronic Excitations +

The most substantial new feature in the VOTCA package is the + addition of explicit quantum-mechanical functionalities in the + VOTCA-XTP part. The added methods aim at a first-principles-based + multiscale modeling of electronically excited states and their + dynamics in complex molecular systems. We very briefly describe the + three main modules of XTP in the following.

+ + Density-Functional Theory +

Excited state calculations require a reference ground state + calculation within density-functional theory. VOTCA-XTP provides + both an automated interface to the ORCA package + (Neese, + 2012) and a lightweight internal density-fucntional theory + (DFT) engine based on atom-centered Gaussian-type orbitals for + method developing and testing. It solves the Kohn-Sham (KS) + Equations for the molecular orbitals + + + ϕnKS(𝐫) + with orbital energies + + εnKS + + + {22m2+Vext(𝐫)+VH(𝐫)+Vxc(𝐫)}ϕnKS(𝐫)=εnKSϕnKS(𝐫), + where + + Vext + is the external potential, + + VH + the Hartree potential, and + + Vxc + the exchange-correlation potential. VOTCA-XTP also contains + functionality for projector-based-embedding DFT-in-DFT ground + state calculations + (Manby + et al., 2012), in which a chosen active subregion of a + molecular system is embedded into an inactive one, reproducing the + total energy of the full system ground state exactly.

+
+ + Many-Body Green’s Functions and the Bethe-Salpeter + Equation +

Using the ground-state reference, many-body Green’s functions + theory with the + + GW + approximation first calculayes single-particle + excitations (electron addition or removal) as solutions + to the quasiparticle (QP) equations + + + {22m2+Vext(𝐫)+VH(𝐫)}ϕnQP(𝐫)+Σ(𝐫,𝐫,εnQP)ϕnQP(𝐫)d𝐫=εnQPϕnQP(𝐫). + In place of the exchange-correlation potential in Eq. + 6, the energy-dependent + self-energy operator + + Σ(𝐫,𝐫,E) + occurs in the QP equations. This operator is evaluated using the + one-body Green’s function in quasi-particle approximation + + + G(𝐫,𝐫,ω)=nϕn(𝐫)ϕn*(𝐫)ωεn+i0+sgn(εnμ) + as + + + Σ(𝐫,𝐫,E)=i2πeiω0+G(𝐫,𝐫,Eω)W(𝐫,𝐫,ω)dω, + where + + W + denotes the dynamically screened Coulomb interaction. Assuming + that + + ϕnQPϕnKS, + the quasiparticle energies can be evaluated perturbatively + according to + + + εnQP=εnKS+ΔεnGW=εnKS+ϕnKS|Σ(εnQP)Vxc|ϕnKS. + As the correction + + ΔεnGW + itself depends on + + εnQP, + Eq. 10 needs + to be solved self-consistently.

+

Neutral excitations with a conserved number of electrons can be + obtained from the Bethe-Salpeter Equation (BSE) by expressing + coupled electron-hole amplitudes of excitation + + + S + in a product basis of single-particle orbitals, i.e., + + + χS(𝐫e,𝐫h)=vocccunoccAvcSϕc(𝐫e)ϕv*(𝐫h)+BvcSϕv(𝐫e)ϕc*(𝐫h), + where + + 𝐫e + ( + + 𝐫h) + is for the electron (hole) coordinate and + + + Avc + ( + + Bvc) + are the expansion coefficients of the excited state wave function + in terms of resonant (anti-resonant) transitions between occupied + + + v + and unoccupied + + c + states, respectively. In this basis, the BSE turns into an + effective two-particle Hamiltonian problem of the form + + + (𝐇_res𝐊_𝐊_𝐇_res)(𝐀S𝐁S)=ΩS(𝐀S𝐁S).

+

Specifically, the matrix elements of the blocks + + + 𝐇_res + and + + 𝐊_ + are calculated as + + + Hvc,vcres=Dvc,vc+ηKvc,vcx+Kvc,vcdKcv,vc=ηKcv,vcx+Kcv,vcd, + with + + + Dvc,vc=(εcεv)δvvδcc,Kvc,vcx=ϕc*(𝐫e)ϕv(𝐫e)vC(𝐫e,𝐫h)ϕc(𝐫h)ϕv*(𝐫h)d3𝐫ed3𝐫hKvc,vcd=ϕc*(𝐫e)ϕc(𝐫e)W(𝐫e,𝐫h,ω=0)ϕv(𝐫h)ϕv*(𝐫h)d3𝐫ed3𝐫h. + and + + η=2 + ( + + η=0) + for singlet (triplet) excitations. Here, + + + Kx + is the repulsive exchange interaction originating from the bare + Coulomb term + + vC, + while the direct interaction + + Kd + contains the attractive, but screened, interaction + + + W + between electron and hole, causing the binding of the + electron-hole pair. In Eq. + 14 it is assumed + that the dynamic properties of + + W(ω) + are negligible, and the computationally less demanding static + approximation + + ω=0 + is employed.

+
+ + Quantum-Classical Embedding +

Polarization effects of an environment can have significant + impact on electronic excitations. As polarization effects are + long-ranged accounting for them requires the treatment of large + systems which is infeasible with explicit quantum methods such as + DFT- + + GW-BSE. + Instead, the system is split into a small part with to + electronically active subsystem to be treated at quantum (QM) + level and a large environment part in which electrostatic and + polarization effects are accounted for in classical models (MM). + In VOTCA-XTP the QM/MM scheme employs distributed atomic multipole + representations for molecules in the MM region, which allows + treatment of both the effects of static electric fields and the + polarization response as a self-consistent reaction field. + Specifically, this classical MM energy for the system is evaluated + as + + + EMM=12A,BABaAbBtu(Qta+ΔQta)TtuabQub, + where + + A + and + + B + indicate individual molecules in the system, + + + a + and + + b + atoms in the respective molecules, + + Qta + are the static atomic multipole moments of rank + + + t + associated to atom + + a, + and + + Ttuab + is the tensor describing the interactions between the multipoles + moments + + Qta + and + + Qub + (Stone, + 2005). The induced moments + + ΔQta + are generated by the electric field created by moments + + + t + of atom + + aa + in molecule + + A + and the one generated by the moment + + u + of atom + + b + in molecule + + B: + + + ΔQta=A,B𝒮ABbBaAaattuαttaaTtuab(Qub+ΔQub), + with + + αttaa + the isotropic atomic polarizability on each site. To avoid effects + of spurious overpolarization, a damped version of the interaction + tensor (Thole damping + (Stone, + 2005)) is used. Then, the static and induced multipoles in + the MM region also interact with the electron density in QM region + via an additional external potential to + Eq.6. At the same time, the + explicit electrostatic field from the QM density is included in + polarizing the MM region.

+
+
+
+ + Code Structure +

For the last couple of years, we have also focused on code + hardening and the introduction of better software engineering + practices. Original VOTCA was designed as modules in separate + repositories, but as many other projects, this turned out to be quite + cumbersome hence we switched to a mono-repo. With recent performance + improvements in the git tools, the benefits of a single repository by + far out-weigh the downside of the very complex workflow of multiple + repositories. The module structure still exists in the source + code.

+

Additionally, we have added continuous integration testing through + GitHub action for 50+ different compiler and operating system + combinations. The also perform continous deployment to the GitHub + Docker registry. And releases get rolled into all major linux + distributions, HomeBrew, Spack and FreeBSD.

+ + Code Modernization +

We did a lot of code refactoring and bumped the C++ standard to + 17. We also modernized our usage of CMake and switched to a mostly + target-base scheme. An attempt to port our particle structure on top + of Cabana + (Slattery + et al., 2022) was made, due to incompatibilties between + Kokkos + (Trott + et al., 2022) and Eigen, we will delay this effort.

+
+ + Updates in VOTCA-CSG +

The particle and molecule data structure were refactored, and we + add support of the H5MD format, which is described below in + details.

+ + H5MD support +

The recent version of VOTCA supports the + H5MD + (de + Buyl et al., 2014) file format, which internally uses + HDF5 + (Koranne, + 2011) storage. This is a very fast and scalable method for + storing molecular trajectories, already implemented in simulation + packages such as LAMMPS + (Thompson + et al., 2022), ESPResSo++ + (Guzman + et al., 2019), and ESPResSo + (Weik + et al., 2019). VOTCA recognizes the trajectory file format + by the extension. In the case of H5MD, it expects a + .h5 extension. Following the H5MD concepts, + the particle trajectories are organized in the + particles container. This container can + handle multiple subsets of the studied system. Therefore, we must + define h5md_particle_group in the XML + topology file to declare which subset of particles to use. The + reader handles both coordinates (if present), forces, and + velocities.

+
+
+ + Design of VOTCA-XTP +

Data structures related to atomistic properties (topology, + molecules, segments, fragments, atoms) in XTP are reused or build + upon those of CSG. Linear algebra related structures and + functionalities are handled by Eigen + (Guennebaud + et al., 2010) which can be accelerated by internally calling + the Intel Math Kernel Library + (Wang + et al., 2014). Exchange-correlation functionals are provided + by the Library of eXchange-Correlation + (LIBXC) functionals + (Lehtola + et al., 2018), while libint + (Valeev, + 2024) and libecpint + (Shaw + & Hill, 2017) are used for the evaluation of molecular + integrals of many-body operators over Gaussian functions.

+

VOTCA–XTP is designed as a library, which is linked to very thin + executables. These executables provide a variety of calculators by + adding keywords on the command line. Virtual interfaces and factory + patterns make the addition of new calculators simple. The same + architecture is used for external DFT and MD codes, making VOTCA–XTP + easily extensible. Lower-level data structures make use of template + metaprogramming to support a variety of data types. VOTCA-XTP + provides different functionalities in three types of + calculator classes:

+ + +

a collection of tools that do not require information of a + mapped MD trajectory, including a specific + DFT- + + GW-BSE + calculator in tools callable by + xtp_tools

+
+ +

analysis and not-high-throughput applications that require a + mapped MD trajectory in calculators + callable by xtp_run

+
+ +

high-throughput, high-performance applications that require a + mapped MD trajectory in jobcalculators + callable by xtp_parallel

+
+
+

In general, VOTCA-XTP uses shared-memory parallelization in the + heavy calculations involving the quantum methods, with the + possibility to seamlessly offload matrix-matrix and matrix-vector + operations to GPU via CUDA.

+ + PyXTP +

The PyXTP python package distributed with VOTCA, contains + python bindings to the main functionalities of VOTCA-XTP. These + python bindings were created using pybind11 + (Jakob + et al., 2017) and provide users with a dedicated Atomistic + Simulation Environment (ASE) + (Larsen + et al., 2017) calculator. The use of this calculator not + only facilitates the adoption of VOTCA-XTP by non-experts users, + but they also allow integrating VOTCA-XTP in the broader ASE + ecosystem.

+

The following snippet of code illustrate the use of PyXTP. This + small code optimize the geometry of a CO molecule in the first + excited singlet states. As seen in the code, the XTP calculator is + used to compute the forces on the nuclei while the geometry + optimization itself is driven by ASE functionalities.

+ from pyxtp import xtp +from ase.io import write +from ase.build import molecule +from ase.optimize import QuasiNewton + +# create a distorted CO molecule +atoms = molecule('CO') +atoms.rattle() + +# instantiate the calculator +calc = xtp(nthreads=2) + +# select the state for which to compute the forces +calc.select_force(energy='singlets', level=0, dynamic=False) + +# this allows to change all options +calc.options.dftpackage.functional = 'PBE' +calc.options.dftpackage.basisset = 'def2-svp' +calc.options.dftpackage.auxbasisset = 'aux-def2-svp' + +# set up the logger +calc.options.logging_file = 'CO_forces.log' + +# set the calculator +atoms.calc = calc + +# optimize the geometry +dyn = QuasiNewton(atoms, trajectory='test.traj') +dyn.run(fmax=0.01) +write('final.xyz', atoms) +
+
+
+ + Acknowledgements +

We acknowledge contributions from Brigitta Sipocz, Syrtis Major, + and Semyeong Oh, and support from Kathryn Johnston during the genesis + of this project. We acknowledge support by the Innovational Research + Incentives Scheme Vidi of the Netherlands Organisation for Scientific + Research (NWO) with project number 723.016.002. Funding is also + provided by NWO and the Netherlands eScience Center for funding + through project number 027.017.G15, within the Joint CSER and eScience + program for Energy Research (JCER 2017). Los Alamos National + Laboratory (LANL) is operated by Triad National Security, LLC, for the + National Nuclear Security Administration of US Department of Energy + (Contract No. 89233218CNA000001). This work is approved for unlimited + release with report number LA-UR-24-25313.

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