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DOE OSTI2021

An Ab Initio Multiple Cloning Method for Non-Adiabatic Excited-State Molecular Dynamics in NWChem

The recently developed ab-initio multiple cloning (AIMC) approach based on the multicongurational Ehrenfest (MCE) method provides a powerful and accurate way of describing the excited-state dynamics of molecular systems. The AIMC method is a controlled approximation to non-adiabatic dynamics with a particular strength in the proper description of decoherence effects due to branching of vibrational wavepackets at a level crossing. In this work, we report a new implementation of the AIMC algorithm in the open source NWChem computational chemistry program. The framework combines linear-response time-dependent density functional theory with Ehrenfest mean-eld theory to determine the equations of motion for classical trajectories. The multi-dimensional wave function is decomposed into a superposition of Gaussian coherent states guided by Ehrenfest trajectories (i.e., MCE approach), which can clone with fully quantum mechanical amplitudes and phases. By using an efficient time-derivative based non-adiabatic coupling approach within the AIMC method, all observable are calculated on-the-y in the non-adiabatic molecular dynamics process. As a representative example, we apply our implementation to study the ultrafast photoinduced electronic and vibrational energy transfer in a pyridine molecule. The effects of the cloning procedure on electronic and vibrational coherence, relaxation and unidirectional energy transfer are discussed. This new AIMC implementation provides a high-level non-adiabatic molecular dynamics framework for simulating photoexcited dynamics in complex molecular systems and experimentally relevant ultrafast spectroscopic probes, such as nonlinear coherent optical and X-ray signals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1994

1919+479: Big WAT in a poor cluster

New x-ray, optical, and redshift data are presented for the cluster of galaxies associated with the giant, 1 Mpc diameter, wide-angle tailed (WAT) radio galaxy 1919+479. The ROSAT Position-Sensitive Proportional Counter (PSPC) pointed observation shows an x-ray peak on the WAT and elongated diffuse emission tracing the galaxy distribution. In addition, an asymmetric extension of emission exists between the tails of the WAT. The fitting of a Raymond-Smith thermal model to the x-ray spectra suggests an approximately = 2 keV temperature intracluster medium (ICM). The cooling time and irregular morphology rule out a cluster-wide cooling flow. The x-ray luminosity and temperature are consistent with the velocity dispersion, 480 km/s, estimated from 31 galaxy velocities. However, this velocity distribution is significantly non-Gaussian, which along with the x-ray morphology, suggests incomplete virialization in the cluster. Substructure analysis does not reveal significant clumping in the velocities/positions; but, the spatial distribution of galaxies is very elongated. Also, the cD galaxy producing the WAT does not have a significant radial peculiar velocity with respect to the cluster centroid. These characteristics are consistent with a merger scenario in which a subcluster has crossed the cluster core in the plane of the sky and has dispersed. We compare this cluster with the post-merger cluster Abell 2634 (Pinkney et al., 1993), containing the prototype WAT, and with a recent N-Body/Hydro simulation of merging clusters. The similarities indicate that the cluster 1919+479 may be the poor extreme of a class of clusters in which the bulk motion in the ICM, caused by a subcluster merger, in shaping the central WAT.

Pinkney, Jason↗

DOE OSTI2022

Multinode Multi-GPU Two-Electron Integrals: Code Generation Using the Regent Language

The computation of two-electron repulsion integrals (ERIs) is often the most expensive step of integral-direct self-consistent field methods. Formally it scales as O(N 4 ), where N is the number of Gaussian basis functions used to represent the molecular wave function. In practice, this scaling can be reduced to O(N 2 ) or less by neglecting small integrals with screening methods. The contributions of the ERIs to the Fock matrix are of Coulomb (J) and exchange (K) type and require separate algorithms to compute matrix elements efficiently. We previously implemented highly efficient GPU-accelerated J-matrix and K-matrix algorithms in the electronic structure code TeraChem. Although these implementations supported the use of multiple GPUs on a node, they did not support the use of multiple nodes. This presents a key bottleneck to cutting-edge ab initio simulations of large systems, e.g., excited state dynamics of photoactive proteins. We present our implementation of multinode multi-GPU J- and K-matrix algorithms in TeraChem using the Regent programming language. Regent directly supports distributed computation in a task-based model and can generate code for a variety of architectures, including NVIDIA GPUs. We demonstrate multinode scaling up to 45 GPUs (3 nodes) and benchmark against hand-coded TeraChem integral code. Finally, we also outline our metaprogrammed Regent implementation, which enables flexible code generation for integrals of different angular momenta.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

The Dark Energy Survey supernova program: cosmological biases from supernova photometric classification

ABSTRACT Cosmological analyses of samples of photometrically identified type Ia supernovae (SNe Ia) depend on understanding the effects of ‘contamination’ from core-collapse and peculiar SN Ia events. We employ a rigorous analysis using the photometric classifier SuperNNova on state-of-the-art simulations of SN samples to determine cosmological biases due to such ‘non-Ia’ contamination in the Dark Energy Survey (DES) 5-yr SN sample. Depending on the non-Ia SN models used in the SuperNNova training and testing samples, contamination ranges from 0.8 to 3.5 per cent, with a classification efficiency of 97.7–99.5 per cent. Using the Bayesian Estimation Applied to Multiple Species (BEAMS) framework and its extension BBC (‘BEAMS with Bias Correction’), we produce a redshift-binned Hubble diagram marginalized over contamination and corrected for selection effects, and use it to constrain the dark energy equation-of-state, w. Assuming a flat universe with Gaussian ΩM prior of 0.311 ± 0.010, we show that biases on w are <0.008 when using SuperNNova, with systematic uncertainties associated with contamination around 10 per cent of the statistical uncertainty on w for the DES-SN sample. An alternative approach of discarding contaminants using outlier rejection techniques (e.g. Chauvenet’s criterion) in place of SuperNNova leads to biases on w that are larger but still modest (0.015–0.03). Finally, we measure biases due to contamination on w0 and wa (assuming a flat universe), and find these to be <0.009 in w0 and <0.108 in wa, 5 to 10 times smaller than the statistical uncertainties for the DES-SN sample.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

A general Bayesian algorithm for the autonomous alignment of beamlines

Autonomous methods to align beamlines can decrease the amount of time spent on diagnostics, and also uncover better global optima leading to better beam quality. The alignment of these beamlines is a high-dimensional expensive-to-sample optimization problem involving the simultaneous treatment of many optical elements with correlated and nonlinear dynamics. Bayesian optimization is a strategy of efficient global optimization that has proved successful in similar regimes in a wide variety of beamline alignment applications, though it has typically been implemented for particular beamlines and optimization tasks. In this paper, we present a basic formulation of Bayesian inference and Gaussian process models as they relate to multi-objective Bayesian optimization, as well as the practical challenges presented by beamline alignment. We show that the same general implementation of Bayesian optimization with special consideration for beamline alignment can quickly learn the dynamics of particular beamlines in an online fashion through hyperparameter fitting with no prior information. We present the implementation of a concise software framework for beamline alignment and test it on four different optimization problems for experiments on X-ray beamlines at the National Synchrotron Light Source II and the Advanced Light Source, and an electron beam at the Accelerator Test Facility, along with benchmarking on a simulated digital twin. We discuss new applications of the framework, and the potential for a unified approach to beamline alignment at synchrotron facilities.

47 OTHER INSTRUMENTATION↗

NASA NTRS2018

Realistic Covariance Generation for the GPM Spacecraft

A covariance realism process for NASA's Global Precipitation Measurement (GPM) spacecraft is detailed. The GPM spacecraft is in a low earth orbit, and performs collision avoidance maneuvers few times a year. Currently GPM is below the International Space Station (ISS). So, in addition to cataloged debris objects, GPM must contend with smallsat/cubesat objects that are deployed from the ISS. Both operational scenarios require complete knowledge of the expected GPM prediction errors as a function of time. In this study, we present a method for generating realistic predicted covariance that uses linear propagation of the covariance with the addition of process noise. Further analyses are presented for the process noise ''tuning'' that generates an inflation factor based on the observed error statistics of the predictive satellite trajectories when compared to the definitive ones. Different tuning strategies are considered and compared via a Goodness-of-Fit testing for the Gaussian properties of the scaled covariance. SpaceNav's realistic covariance generation approach takes into account the contribution of predicted maneuver errors in the increased propagation uncertainty. Corresponding maneuver uncertainty is injected into the state uncertainty, and is used within the collision avoidance process to determine the collision risk for close approach events that follow a maneuver. This is a critical step in the maneuver planning process that provides the satellite operator with an accurate quantification of the collision probability for planned maneuvers. Using this information, an informed decision can be made to proceed with a maneuver if the collision risk is acceptable. This approach is validated by Monte-Carlo simulations and results are presented.

spacecraft uncertainty propagation↗

DOE OSTI2021

Operator learning for predicting multiscale bubble growth dynamics

We report simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein, we develop a framework based on operator regression, the so-called deep operator network (DeepONet), with the long-term objective to simplify multiscale modeling by avoiding the fragile and time-consuming “hand-shaking” interface algorithms for stitching together heterogeneous descriptions of multiscale phenomena. To this end, as a first step, we investigate if a DeepONet can learn the dynamics of different scale regimes, one at the deterministic macroscale and the other at the stochastic microscale regime with inherent thermal fluctuations. Specifically, we test the effectiveness and accuracy of the DeepONet in predicting multirate bubble growth dynamics, which is described by a Rayleigh–Plesset (R–P) equation at the macroscale and modeled as a stochastic nucleation and cavitation process at the microscale by dissipative particle dynamics (DPD). First, we generate data using the R–P equation for multirate bubble growth dynamics caused by randomly time-varying liquid pressures drawn from Gaussian random fields (GRFs). Our results show that properly trained DeepONets can accurately predict the macroscale bubble growth dynamics and can outperform long short-term memory networks. We also demonstrate that the DeepONet can extrapolate accurately outside the input distribution using only very few new measurements. Subsequently, we train the DeepONet with DPD data corresponding to stochastic bubble growth dynamics. Although the DPD data are noisy and we only collect sparse data points on the trajectories, the trained DeepONet model is able to predict accurately the mean bubble dynamics for time-varying GRF pressures. Taken together, our findings demonstrate that DeepONets can be employed to unify the macroscale and microscale models of the multirate bubble growth problem, hence providing new insight into the role of operator regression via DNNs in tackling realistic multiscale problems and in simplifying modeling with heterogeneous descriptions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Beyond the Debye–Hückel limit: Toward a general theory for concentrated electrolytes

The phenomenon of underscreening in concentrated electrolyte solutions leads to a larger decay length of the charge–charge correlation than the prediction of Debye–Hückel (DH) theory and has found a resurgence of both theoretical and experimental interest in the chemical physics community. To systematically understand and investigate this phenomenon in electrolytes requires a theory of concentrated electrolytes to describe charge–charge correlations beyond the DH theory. We review the theories of electrolytes that can transition from the DH limit to concentrations where charge correlations dominate, giving rise to underscreening and the associated Kirkwood Transitions (KTs). In this perspective, we provide a conceptual approach to a theoretical formulation of electrolyte solutions that exploits the competition between molecular-informed short-range (SR) and long-range interactions. We demonstrate that all deviations from the DH limit for real electrolyte solutions can be expressed through a single function ΣQ that can be determined both theoretically and numerically. Importantly, ΣQ can be directly related to the details of SR interactions and, therefore, can be used as a tool to understand how differences in representations of interaction can influence collective effects. The precise function form of ΣQ can be inferred through a Gaussian field theory of both the number and charge densities. The resulting formulation is validated by experiment and can accurately describe the collective phenomenon of screening in concentrated bulk electrolytes. Importantly, the Gaussian field theory predictions of the screening lengths appear to be less than ∼1 nm at concentrations above KTs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2022

Galaxy Correlation Function and Local Density from Photometric Redshifts Using the Stochastic Order Redshift Technique (SORT)

The stochastic order redshift technique (SORT) is a simple, efficient, and robust method to improve cosmological redshift measurements. The method relies upon having a small (∼10 per cent) reference sample of high-quality redshifts. Within pencil- beam-like sub-volumes surrounding each galaxy, we use the precise dN/dz distribution of the reference sample to recover new redshifts and assign them one-to-one to galaxies such that the original rank order of redshifts is preserved. Preserving the rank order is motivated by the fact that random variables drawn from Gaussian probability density functions with different means but equal standard deviations satisfy stochastic ordering. This process is repeated for sub-volumes surrounding each galaxy in the survey. This results in every galaxy being assigned multiple ‘recovered’ redshifts from which a new redshift estimate is determined. An earlier paper applied SORT to a mock Sloan Digital Sky Survey at z 0.2 and accurately recovered the two-point correlation function (2PCF) on scales > 4 h−1Mpc. In this paper, we test the performance of SORT in surveys spanning the redshift range 0.75 < z < 2.25. We used two mock surveys extracted from the Small MultiDark–Planck and Bolshoi–Planck N-body simulations with dark matter haloes that were populated by the Santa Cruz semi-analytic model. We find that SORT overall improves redshift estimates, accurately recovers the redshift-space 2PCF ξ (s) on scales > 2.5 h−1Mpc, and provides improved local density estimates in regions of average or higher density, which may allow for improved understanding of how galaxy properties relate to their environments.

James Kakos↗

DOE OSTI2023

Parameter estimation with maximal updated densities

A recently developed measure-theoretic framework solves a stochastic inverse problem (SIP) for models where uncertainties in model output data are predominantly due to aleatoric (i.e., irreducible) uncertainties in model inputs (i.e., parameters). The subsequent inferential target is a distribution on parameters. Another type of inverse problem is to quantify uncertainties in estimates of “true” parameter values under the assumption that such uncertainties should be reduced as more data are incorporated into the problem, i.e., the uncertainty is considered epistemic. A major contribution of this work is the formulation and solution of such a parameter identification problem (PIP) within the measure-theoretic framework developed for the SIP. The approach is novel in that it utilizes a solution to a stochastic forward problem (SFP) to update an initial density only in the parameter directions informed by the model output data. In other words, this method performs “selective regularization” only in the parameter directions not informed by data. Further, the solution is defined by a maximal updated density (MUD) point where the updated density defines the measure-theoretic solution to the PIP. Another significant contribution of this work is the full theory of existence and uniqueness of MUD points for linear maps with Gaussian distributions. Data-constructed Quantity of Interest (QoI) maps are also presented and analyzed for solving the PIP within this measure-theoretic framework as a means of reducing uncertainties in the MUD estimate. We conclude with a demonstration of the general applicability of the method on two problems involving either spatial or temporal data for estimating uncertain model parameters. The first problem utilizes spatial data from a stationary partial differential equation to produce a MUD estimate of an uncertain boundary condition. The second problem utilizes temporal data obtained from the state-of-the-art ADvanced CIRCulation (ADCIRC) model to obtain a MUD estimate of uncertain wind drag coefficients for a simulated extreme weather event near the Shinnecock Inlet located in the Outer Barrier of Long Island, NY, USA.

42 ENGINEERING↗

DOE OSTI2021

On the Bandwidth and Beam Profile Characteristics of a Simple Low-Frequency Collimated Ultrasound Beam Source

We numerically investigate the bandwidth and collimation characteristics of ultrasound beams generated by a simple collimated ultrasound beam source that consists of a piezoelectric disk operated near its radial mode resonances. We simulate the ultrasound beam generated in a fluid medium as a function of the excitation frequency for two cases: (1) free piezoelectric disk that corresponds to zero-traction along the lateral edge and (2) fixed piezoelectric disk that corresponds to zero-displacement along the lateral edge. We present and discuss the physical mechanism underpinning the frequency-dependent collimation and bandwidth properties of the ultrasound beams. We observe that the collimated beam generated by the free disk repeatedly lengthens/shortens and also extends/retracts sidelobes with increasing frequency. Alternatively, fixing the piezoelectric disk results in a consistent beam profile shape across a broad range of frequencies. This facilitates generating broadband signals such as a Gaussian pulse or chirp, which are common in ultrasound imaging. Thus, the fixed piezoelectric disk finds application as a collimated ultrasound beam source in a wide range of applications including medical ultrasound imaging, scanning acoustic microscopy, sonar detection, and other nondestructive ultrasound inspection techniques.

47 OTHER INSTRUMENTATION↗

NASA NTRS2003

Self-Consistent Model of Magnetospheric Ring Current and Electromagnetic Ion Cyclotron Waves: The May 2-7, 1998, Storm

Complete description of a self-consistent model for magnetospheric ring current interacting with electromagnetic ion cyclotron waves is presented. The model is based on the system of two kinetic equations; one equation describes the ring current ion dynamics, and another equation describes the wave evolution. The effects on ring current ions interacting with electromagnetic ion cyclotron waves, and back on waves, are considered self-consistently by solving both equations on a global magnetospheric scale under non steady-state conditions. In the paper by Khazanov et al. [2002] this self-consistent model has only been shortly outlined, and discussions of many the model related details have been omitted. For example, in present study for the first time a new algorithm for numerical finding of the resonant numbers for quasilinear wave-particle interaction is described, or it is demonstrated that in order to describe quasilinear interaction in a multi-ion thermal plasma correctly, both e and He(+) modes of electromagnetic ion cyclotron waves should be employed. The developed model is used to simulate the entire May 2-7, 1998 storm period. Trapped number fluxes of the ring current protons are calculated and presented along with their comparison with the data measured by the 3D hot plasma instrument Polar/HYDRA. Examining of the wave (MLT, L shell) distributions produced during the storm progress reveals an essential intensification of the wave emissions in about two days after main phase of storm. This result is well consistent with the earlier ground-based observations. Also the theoretical shapes and the occurrence rates for power spectral densities of electromagnetic ion cyclotron waves are studied. It is found that in about 2 days after the storm main phase on May 4, mainly non Gaussian shapes of power spectral densities are produced.

Khazanov, G. V.↗

DOE OSTI2023

Automated Design-for-Reliability of a Power Electronics Module

The design of a power electronics module is a multiphysics problem and involves electrical, thermal, and reliability targets and constraints. Although the electrical and thermal design consider multiple aspects such as materials, geometry, and energy losses, reliability design is often limited to the selection of the attachment materials and electrical interconnect types. In this paper, we incorporate reliability metrics in the design phase by investigating the impact of package geometry on the thermomechanical behavior of the die-attachment material. To this end, we conducted thermal and power cycling simulations of a commercial six-pack power module with silicon carbide devices to compute junction temperature and strain energy density per cycle, respectively. We performed multiple simulations with different geometric dimensions and established a correlation between input features and output variables using subspace-based dimension reduction. The machine learning-based dimension reduction method serves as a surrogate model, which can be employed to identify the optimal module design from a thermal and reliability standpoint.

design-for-reliability↗

DOE OSTI2024

Estimating Sparse Direct Effects in Multivariate Regression With the Spike-and-Slab LASSO

The multivariate regression interpretation of the Gaussian chain graph model simultaneously parametrizes (i) the direct effects of p predictors on q outcomes and (ii) the residual partial covariances between pairs of outcomes. We introduce a new method for fitting sparse versions of these models with spike-and-slab LASSO (SSL) priors. We develop an Expectation Conditional Maximization algorithm to obtain sparse estimates of the p × q matrix of direct effects and the q × q residual precision matrix. Our algorithm iteratively solves a sequence of penalized maximum likelihood problems with self-adaptive penalties that gradually filter out negligible regression coefficients and partial covariances. Because it adaptively penalizes individual model parameters, our method is seen to outperform fixed-penalty competitors on simulated data. We establish the posterior contraction rate for our model, buttressing our method’s excellent empirical performance with strong theoretical guarantees. Using our method, we estimated the direct effects of diet and residence type on the composition of the gut microbiome of elderly adults.

EM algorithm↗

DOE OSTI2024

Chemical evolution of local post-starburst galaxies: implications for the mass–metallicity relation

ABSTRACT We use the stellar fossil record to constrain the stellar metallicity evolution and star-formation histories of the post-starburst (PSB) regions within 45 local PSB galaxies from the MaNGA survey. The direct measurement of the regions’ stellar metallicity evolution is achieved by a new two-step metallicity model that allows for stellar metallicity to change at the peak of the starburst. We also employ a Gaussian process noise model that accounts for correlated errors introduced by the observational data reduction or inaccuracies in the models. We find that a majority of PSB regions (69 per cent at >1σ significance) increased in stellar metallicity during the recent starburst, with an average increase of 0.8 dex and a standard deviation of 0.4 dex. A much smaller fraction of PSBs are found to have remained constant (22 per cent) or declined in metallicity (9 per cent, average decrease 0.4 dex, standard deviation 0.3 dex). The pre-burst metallicities of the PSB galaxies are in good agreement with the mass–metallicity (MZ) relation of local star-forming galaxies. These results are consistent with hydrodynamic simulations, which suggest that mergers between gas-rich galaxies are the primary formation mechanism of local PSBs, and rapid metal recycling during the starburst outweighs the impact of dilution by any gas inflows. The final mass-weighted metallicities of the PSB galaxies are consistent with the MZ relation of local passive galaxies. Our results suggest that rapid quenching following a merger-driven starburst is entirely consistent with the observed gap between the stellar mass–metallicity relations of local star-forming and passive galaxies.

Leung, Ho-Hin (ORCID:0000000304865178)↗

NASA NTRS1977

The low-latitude circulation of Mars

A steady-state two-layer atmospheric model is used in an attempt to simulate the circulation of the equatorial regions of Mars, with consideration of both thermal and mechanical orographic effects. A steady-state solution is sought with the aim of producing mean seasonal circulations upon which tides can be superimposed, and the relative importance of orographic forcing at low latitudes is evaluated. It is assumed that the atmospheres over a topographic feature and over flat terrain possess the same radiative and convective properties, simple dissipation laws are introduced which represent a surface drag effect, and six first-order difference equations are obtained and then reduced to two linear complex second-order coupled difference equations. Analysis of the response of the equinoctial basic wind field to a Gaussian orographic feature situated at the equator and zero deg longitude reveals a number of similarities and differences between the Martian and terrestrial responses. Most of the similarities are explained in terms of the dynamics of a rotating atmosphere, while the major differences are at least partially explained by the different optical properties, lower boundaries, and smaller mass of the Martian atmosphere.

Webster, P. J.↗

NASA NTRSDate not supplied

Estimation With Range Dependent Sensor Model

This paper focuses on the improvement of target tracking accuracy taking into account the sensor’s reading degradation as the relative range increases. The approach is based on the assumption that range measurement error depends on the actual range. Specifically, we model the measurement error as a proportional to the actual range term plus a zero-mean, Gaussian distributed, and uncorrelated process. We present two approaches to tracking a target with constant velocity model. The first approach uses Extended Kalman Filter (EKF) framework to estimate target's states and the unknown proportionality coefficient with linearization on the observation model on the predicted states at each time step. The second one uses a measurement conversion method to estimate the target's scaled by the unknown constant term states, which is shown to be unbiased. This conversion results in linear state and observation models, hence the standard Kalman filter can be applied. The actual target state is computed by application of back scaling with the estimate of unknown scale factor. We evaluate the approaches in desktop simulations.

Target tracking↗

DOE OSTI2020

The many-body expansion for aqueous systems revisited: 1. Water-water interactions

We revisit the Many-Body Expansion (MBE) for water-water interactions by examining the effects of the basis set, including those resulting from the Basis Set Superposition Error (BSSE) correction, on the various terms for selected sizes of water clusters up to n = 21. The analysis is performed at the second order Møller-Plesset (MP2) perturbation theory with the family of augmented correlation consistent basis sets up to five zeta quality for the (H2O)n, n = 7, 10, 13, 16 and 21 clusters, for which we report either the complete MBE (n = 7, 10) or the one through the 6-body (n = 13) and the 5-body terms (n = 16, 21). Our results suggest that any sizeable contributions to the total cluster binding energy arising from the 5-body and larger terms are solely an artifact of the size of the basis set. Indeed, all terms above the 4-body converge monotonically to practically zero at the Complete Basis Set (CBS) limit. The magnitudes of the 5-body and above terms are accurately reproduced even with the smaller basis set of the series (aug-cc-pVDZ) once the BSSE correction is taken into account. The same level of theory (MP2/aug-cc-pVDZ, BSSEcorrected) also accurately reproduces the MP2/CBS values of the 3- and 4-body terms. The contribution of electron correlation to the 3- and 4-body terms is quite small, so that neglecting the correlation contribution in all terms above the 3-body results in an error of ??(0.1%). The BSSE correction to the largest 2-body term in the MBE was accurately estimated from the function ?? [1 + erf(-?? ??)], which is proportional to the common (overlapping) area between two Gaussian distributions whose centers are separated by R, with the constants ??, ?? fitted to the calculated BSSE corrections for the individual 2-body terms of the clusters with each basis set. Our results unquestionably demonstrate that the MBE for water-water interactions converges to the 4-body term, since any finite terms above the 4-body are artifacts of the size of the basis set and can be safely truncated at the 4-body term when either a very large basis set is used or BSSE corrections are taken into account even with the aug-cc-pVDZ basis set. We expect these findings to have important consequences in the pursuit of accurate many-body molecular dynamics simulations for aqueous systems.

Heindel, Joseph↗