Density Functional Theory Cost Research Articles

Accurate structures and rotational constants of bicyclic monoterpenes at DFT cost by means of the bond-corrected Pisa composite scheme (BPCS).

The structural, conformational, and spectroscopic properties in the gas phase of 20 bicyclic monoterpenes and monoterpenoids have been analyzed by a new accurate, reduced-cost computational strategy. In detail, the revDSD-PBEP86 double-hybrid functional in conjunction with the D3BJ empirical dispersion corrections and a suitable triple-zeta basis set provides accurate geometrical parameters, whence equilibrium rotational constants, which are further improved by proper account of core-valence correlation. Average deviations within 0.1% between computed and experimental rotational constants are reached when taking into account the vibrational corrections obtained by the B3LYP functional in conjunction with a double-zeta basis set in the framework of second-order vibrational perturbation theory. In addition to their intrinsic interest, the studied terpenes further extend the panel of systems for which the proposed strategy has provided accurate results at density functional theory cost. Therefore, a very accurate yet robust and user-friendly tool is now available for systematic investigations of the role of stereo-electronic effects on the properties of large systems of current technological and/or biological interest by experimentally oriented researchers.

Best-of-Both-Worlds Predictive Approach to Dissociative Chemisorption on Metals.

Predictive capability, accuracy, and affordability are essential features of a theory that is capable of describing dissociative chemisorption on a metal surface. This type of reaction is important for heterogeneous catalysis. Here we present an approach in which we use diffusion Monte Carlo (DMC) to pin the minimum barrier height and construct a density functional that reproduces this value. This predictive approach allows the construction of a potential energy surface at the cost of density functional theory while retaining near DMC accuracy. Scrutinizing effects of energy dissipation and quantum tunneling, dynamics calculations suggest the approach to be of near chemical accuracy, reproducing molecular beam sticking experiments for the showcase H2 + Al(110) system to ∼1.4 kcal/mol.

Accelerating Non-Empirical Structure Determination of Ziegler–Natta Catalysts with a High-Dimensional Neural Network Potential

The determination of catalyst nanostructures with first-principles accuracy using genetic algorithms (GA) is very demanding due to the cubic scaling of the computational cost of density functional theory (DFT) calculations. Here, we demonstrate, for the case of Ziegler–Natta MgCl2/TiCl4 nanoplates, how this structure determination can be accelerated by employing a high-dimensional neural network potential (HDNNP) of essentially DFT accuracy. First, when building HDNNPs for MgCl2/TiCl4 clusters with computationally tractable sizes, we found that the structural diversity in the training set is crucial for obtaining HDNNPs reliably describing the large variety of structures generated by GA. The resulting HDNNPs dramatically accelerated the structure determination while yielding results consistent with DFT. Subsequently, we developed a multistep adaptive procedure to construct a HDNNP for MgCl2/TiCl4 clusters consistent in size and TiCl4 coverage with experiments where prior DFT results were scarcely collected. The structure determination and analyses underline the importance of system size and composition in order to predict some experimentally known facts such as the surface morphology and population of isospecific sites.

Graph-Theoretic Molecular Fragmentation for Potential Surfaces Leads Naturally to a Tensor Network Form and Allows Accurate and Efficient Quantum Nuclear Dynamics.

Molecular fragmentation methods have revolutionized quantum chemistry. Here, we use a graph-theoretically generated molecular fragmentation method, to obtain accurate and efficient representations for multidimensional potential energy surfaces and the quantum time-evolution operator, which plays a critical role in quantum chemical dynamics. In doing so, we find that the graph-theoretic fragmentation approach naturally reduces the potential portion of the time-evolution operator into a tensor network that contains a stream of coupled lower-dimensional propagation steps to potentially achieve quantum dynamics with reduced complexity. Furthermore, the fragmentation approach used here has previously been shown to allow accurate and efficient computation of post-Hartree-Fock electronic potential energy surfaces, which in many cases has been shown to be at density functional theory cost. Thus, by combining the advantages of molecular fragmentation with the tensor network formalism, the approach yields an on-the-fly quantum dynamics scheme where both the electronic potential calculation and nuclear propagation portion are enormously simplified through a single stroke. The method is demonstrated by computing approximations to the propagator and to potential surfaces for a set of coupled nuclear dimensions within a protonated water wire problem exhibiting the Grotthuss mechanism of proton transport. In all cases, our approach has been shown to reduce the complexity of representing the quantum propagator, and by extension action of the propagator on an initial wavepacket, by several orders, with minimal loss in accuracy.

Graph Theoretic Molecular Fragmentation for Multidimensional Potential Energy Surfaces Yield an Adaptive and General Transfer Machine Learning Protocol.

Over a series of publications we have introduced a graph-theoretic description for molecular fragmentation. Here, a system is divided into a set of nodes, or vertices, that are then connected through edges, faces, and higher-order simplexes to represent a collection of spatially overlapping and locally interacting subsystems. Each such subsystem is treated at two levels of electronic structure theory, and the result is used to construct many-body expansions that are then embedded within an ONIOM-scheme. These expansions converge rapidly with many-body order (or graphical rank) of subsystems and have been previously used for ab initio molecular dynamics (AIMD) calculations and for computing multidimensional potential energy surfaces. Specifically, in all these cases we have shown that CCSD and MP2 level AIMD trajectories and potential surfaces may be obtained at density functional theory cost. The approach has been demonstrated for gas-phase studies, for condensed phase electronic structure, and also for basis set extrapolation-based AIMD. Recently, this approach has also been used to derive new quantum-computing algorithms that enormously reduce the quantum circuit depth in a circuit-based computation of correlated electronic structure. In this publication, we introduce (a) a family of neural networks that act in parallel to represent, efficiently, the post-Hartree-Fock electronic structure energy contributions for all simplexes (fragments), and (b) a new k-means-based tessellation strategy to glean training data for high-dimensional molecular spaces and minimize the extent of training needed to construct this family of neural networks. The approach is particularly useful when coupled cluster accuracy is desired and when fragment sizes grow in order to capture nonlocal interactions accurately. The unique multidimensional k-means tessellation/clustering algorithm used to determine our training data for all fragments is shown to be extremely efficient and reduces the needed training to only 10% of data for all fragments to obtain accurate neural networks for each fragment. These fully connected dense neural networks are then used to extrapolate the potential energy surface for all molecular fragments, and these are then combined as per our graph-theoretic procedure to transfer the learning process to a full system energy for the entire AIMD trajectory at less than one-tenth the cost as compared to a regular fragmentation-based AIMD calculation.

Graph-Theory-Based Molecular Fragmentation for Efficient and Accurate Potential Surface Calculations in Multiple Dimensions.

We present a multitopology molecular fragmentation approach, based on graph theory, to calculate multidimensional potential energy surfaces in agreement with post-Hartree-Fock levels of theory but at the density functional theory cost. A molecular assembly is coarse-grained into a set of graph-theoretic nodes that are then connected with edges to represent a collection of locally interacting subsystems up to an arbitrary order. Each of the subsystems is treated at two levels of electronic structure theory, the result being used to construct many-body expansions that are embedded within an ONIOM scheme. These expansions converge rapidly with the many-body order (or graphical rank) of subsystems and capture many-body interactions accurately and efficiently. However, multiple graphs, and hence multiple fragmentation topologies, may be defined in molecular configuration space that may arise during conformational sampling or from reactive, bond breaking and bond formation, events. Obtaining the resultant potential surfaces is an exponential scaling proposition, given the number of electronic structure computations needed. We utilize a family of graph-theoretic representations within a variational scheme to obtain multidimensional potential surfaces at a reduced cost. The fast convergence of the graph-theoretic expansion with increasing order of many-body interactions alleviates the exponential scaling cost for computing potential surfaces, with the need to only use molecular fragments that contain a fewer number of quantum nuclear degrees of freedom compared to the full system. This is because the dimensionality of the conformational space sampled by the fragment subsystems is much smaller than the full molecular configurational space. Additionally, we also introduce a multidimensional clustering algorithm, based on physically defined criteria, to reduce the number of energy calculations by orders of magnitude. The molecular systems benchmarked include coupled proton motion in protonated water wires. The potential energy surfaces and multidimensional nuclear eigenstates obtained are shown to be in very good agreement with those from explicit post-Hartree-Fock calculations that become prohibitive as the number of quantum nuclear dimensions grows. The developments here provide a rigorous and efficient alternative to this important chemical physics problem.

First principles reactive simulation for equation of state prediction.

The high cost of density functional theory (DFT) has hitherto limited the ab initio prediction of the equation of state (EOS). In this article, we employ a combination of large scale computing, advanced simulation techniques, and smart data science strategies to provide an unprecedented ab initio performance analysis of the high explosive pentaerythritol tetranitrate (PETN). Comparison to both experiment and thermochemical predictions reveals important quantitative limitations of DFT for EOS prediction and thus the assessment of high explosives. In particular, we find that DFT predicts the energy of PETN detonation products to be systematically too high relative to the unreacted neat crystalline material, resulting in an underprediction of the detonation velocity, pressure, and temperature at the Chapman-Jouguet state. The energetic bias can be partially accounted for by high-level electronic structure calculations of the product molecules. We also demonstrate a modeling strategy for mapping chemical composition across a wide parameter space with limited numerical data, the results of which suggest additional molecular species to consider in thermochemical modeling.

Modeling of the spectroscopy of core electrons with density functional theory

AbstractThe availability of X‐ray light sources with increased resolution and intensity has provided a foundation for increasingly sophisticated experimental studies exploiting the spectroscopy of core electrons to probe fundamental chemical, physical, and biological processes. Quantum chemical calculations can play a critical role in the analysis of these experimental measurements. The relatively low computational cost of density functional theory (DFT) and time‐dependent density functional theory (TDDFT) make them attractive choices for simulating the spectroscopy of core electrons. An overview of current developments to apply DFT and TDDFT to study the key techniques of X‐ray photoelectron spectroscopy, X‐ray absorption spectroscopy, X‐ray emission spectroscopy, and resonant inelastic X‐ray scattering is presented. Insight into the accuracy that can be achieved, in conjunction with an examination of the limitations and challenges to modeling the spectroscopy of core electrons with DFT is provided.This article is categorized under:Electronic Structure Theory > Ab Initio Electronic Structure MethodsTheoretical and Physical Chemistry > SpectroscopyElectronic Structure Theory > Density Functional Theory

First-principles adaptive-boost accelerated molecular dynamics simulation with effective boost potential construction methods: a study of Li diffusion in Si crystal

First-principles molecular dynamics (FPMD) simulation is a powerful tool for studying the mechanical, chemical, and thermal properties of materials. However, because of the fundamental time-scale limitation of molecular dynamics and the high computational cost of density functional theory, many of the rare events that dominate these properties cannot be directly investigated. Several methods of accelerating FPMD calculations have been developed to analyze these rare events, but to the best of the authors’ knowledge, no quantitative computation of event rate and activation free energy has been achieved. Here, we have developed an accelerated FPMD based on FPMD and the adaptive boost method (Ishii et al. Phys. Rev. B 85, 064303 (2012)), which remove the fundamental drawback of FPMD: time-scale limitation. We also propose a novel boost potential construction algorithms that allows an accurate boost potential to be constructed with a limited number of FPMD samplings. In this study, to confirm the validity of the method, we compute the diffusion of a Li atom in a Si crystal. The temperature-dependent diffusivity was obtained and the activation enthalpy was calculated from an Arrhenius plot and compared with reported experimental diffusivities.

Accurate prediction of core-level spectra of radicals at density functional theory cost via square gradient minimization and recoupling of mixed configurations.

State-specific orbital optimized approaches are more accurate at predicting core-level spectra than traditional linear-response protocols, but their utility had been restricted due to the risk of "variational collapse" down to the ground state. We employ the recently developed square gradient minimization [D. Hait and M. Head-Gordon, J. Chem. Theory Comput. 16, 1699 (2020)] algorithm to reliably avoid variational collapse and study the effectiveness of orbital optimized density functional theory (DFT) at predicting second period element 1s core-level spectra of open-shell systems. Several density functionals (including SCAN, B3LYP, and ωB97X-D3) are found to predict excitation energies from the core to singly occupied levels with high accuracy (≤0.3 eV RMS error) against available experimental data. Higher excited states are, however, more challenging by virtue of being intrinsically multiconfigurational. We thus present a configuration interaction inspired route to self-consistently recouple single determinant mixed configurations obtained from DFT, in order to obtain approximate doublet states. This recoupling scheme is used to predict the C K-edge spectra of the allyl radical, the O K-edge spectra of CO+, and the N K-edge of NO2 with high accuracy relative to experiment, indicating substantial promise in using this approach for the computation of core-level spectra for doublet species [vs more traditional time dependent DFT, equation of motion coupled cluster singles and doubles (EOM-CCSD), or using unrecoupled mixed configurations]. We also present general guidelines for computing core-excited states from orbital optimized DFT.

Highly Accurate Prediction of Core Spectra of Molecules at Density Functional Theory Cost: Attaining Sub-electronvolt Error from a Restricted Open-Shell Kohn-Sham Approach.

We present the use of the recently developed square gradient minimization (SGM) algorithm for excited-state orbital optimization to obtain spin-pure restricted open-shell Kohn-Sham (ROKS) energies for core excited states of molecules. The SGM algorithm is robust against variational collapse and offers a reliable route to converging orbitals for target excited states at only 2-3 times the cost of ground-state orbital optimization (per iteration). ROKS/SGM with the modern SCAN/ωB97X-V functionals is found to predict the K-edge of C, N, O, and F to a root mean squared error of ∼0.3 eV. ROKS/SGM is equally effective at predicting L-edge spectra of third period elements, provided a perturbative spin-orbit correction is employed. This high accuracy can be contrasted with traditional time-dependent density functional theory (TDDFT), which typically has greater than 10 eV error and requires translation of computed spectra to align with experiment. ROKS is computationally affordable (having the same scaling as ground-state DFT and a slightly larger prefactor) and can be applied to geometry optimizations/ab initio molecular dynamics of core excited states, as well as condensed phase simulations. ROKS can also model doubly excited/ionized states with one broken electron pair, which are beyond the ability of linear response based methods.

SoftBV - a software tool for screening the materials genome of inorganic fast ion conductors.

The identification of materials for advanced energy-storage systems is still mostly based on experimental trial and error. Increasingly, computational tools are sought to accelerate materials discovery by computational predictions. Here are introduced a set of computationally inexpensive software tools that exploit the bond-valence-based empirical force field previously developed by the authors to enable high-throughput computational screening of experimental or simulated crystal-structure models of battery materials predicting a variety of properties of technological relevance, including a structure plausibility check, surface energies, an inventory of equilibrium and interstitial sites, the topology of ion-migration paths in between those sites, the respective migration barriers and the site-specific attempt frequencies. All of these can be predicted from CIF files of structure models at a minute fraction of the computational cost of density functional theory (DFT) simulations, and with the added advantage that all the relevant pathway segments are analysed instead of arbitrarily predetermined paths. The capabilities and limitations of the approach are evaluated for a wide range of ion-conducting solids. An integrated simple kinetic Monte Carlo simulation provides rough (but less reliable) predictions of the absolute conductivity at a given temperature. The automated adaptation of the force field to the composition and charge distribution in the simulated material allows for a high transferability of the force field within a wide range of Lewis acid-Lewis base-type ionic inorganic compounds as necessary for high-throughput screening. While the transferability and precision will not reach the same levels as in DFT simulations, the fact that the computational cost is several orders of magnitude lower allows the application of the approach not only to pre-screen databases of simple structure prototypes but also to structure models of complex disordered or amorphous phases, and provides a path to expand the analysis to charge transfer across interfaces that would be difficult to cover by ab initio methods.

Use of Density Functional Based Tight Binding Methods in Vibrational Circular Dichroism.

Vibrational circular dichroism (VCD) is a spectroscopic technique used to resolve the absolute configuration of chiral systems. Obtaining a theoretical VCD spectrum requires computing atomic polar and axial tensors on top of the computationally demanding construction of the force constant matrix. In this study we evaluated a VCD model in which all necessary quantities are obtained with density functional based tight binding (DFTB) theory. The analyzed DFTB parametrizations fail at providing accurate vibrational frequencies and electric dipole gradients but yield reasonable normal modes at a fraction of the computational cost of density functional theory (DFT). Thus, by applying DFTB in composite methods along with DFT, we show that it is possible to obtain accurate VCD spectra at a much lower computational demand.

Is It Possible To Obtain Coupled Cluster Quality Energies at near Density Functional Theory Cost? Domain-Based Local Pair Natural Orbital Coupled Cluster vs Modern Density Functional Theory.

The recently developed domain-based local pair natural orbital coupled cluster theory with single, double, and perturbative triple excitations (DLPNO-CCSD(T)) delivers results that are closely approaching those of the parent canonical coupled cluster method at a small fraction of the computational cost. A recent extended benchmark study established that, depending on the three main truncation thresholds, it is possible to approach the canonical CCSD(T) results within 1 kJ (default setting, TightPNO), 1 kcal/mol (default setting, NormalPNO), and 2-3 kcal (default setting, LoosePNO). Although thresholds for calculations with TightPNO are 2-4 times slower than those based on NormalPNO thresholds, they are still many orders of magnitude faster than canonical CCSD(T) calculations, even for small and medium sized molecules where there is little locality. The computational effort for the coupled cluster step scales nearly linearly with system size. Since, in many instances, the coupled cluster step in DLPNO-CCSD(T) is cheaper or at least not much more expensive than the preceding Hartree-Fock calculation, it is useful to compare the method against modern density functional theory (DFT), which requires an effort comparable to that of Hartree-Fock theory (at least if Hartree-Fock exchange is part of the functional definition). Double hybrid density functionals (DHDF's) even require a MP2-like step. The purpose of this article is to evaluate the cost vs accuracy ratio of DLPNO-CCSD(T) against modern DFT (including the PBE, B3LYP, M06-2X, B2PLYP, and B2GP-PLYP functionals and, where applicable, their van der Waals corrected counterparts). To eliminate any possible bias in favor of DLPNO-CCSD(T), we have chosen established benchmark sets that were specifically proposed for evaluating DFT functionals. It is demonstrated that DLPNO-CCSD(T) with any of the three default thresholds is more accurate than any of the DFT functionals. Furthermore, using the aug-cc-pVTZ basis set and the LoosePNO default settings, DLPNO-CCSD(T) is only about 1.2 times slower than B3LYP. With NormalPNO thresholds, DLPNO-CCSD(T) is about a factor of 2 slower than B3LYP and shows a mean absolute deviation of less than 1 kcal/mol to the reference values for the four different data sets used. Our conclusion is that coupled cluster energies can indeed be obtained at near DFT cost.

A Caveat on SCC-DFTB and Noncovalent Interactions Involving Sulfur Atoms.

Accurate modeling of noncovalent interactions involving sulfur today is ubiquitous, particularly with regard to the role played by sulfur-containing heterocycles in the field of organic electronics. The density functional tight binding (DFTB) method offers a good compromise between computational efficiency and accuracy, enabling the treatment of thousands of atoms at a fraction of the cost of density functional theory (DFT) evaluations. DFTB is an approximate quantum chemical approach that is based on the DFT total energy expression. Here, we address a critical issue inherent to the DFTB parametrization, which prevents the use of the DFTB framework for simulating noncovalent interactions involving sulfur atoms and precludes its combination with a dispersion correction. (1-5) Dramatic examples of structural patterns relevant to the field of organic electronics illustrate that DFTB delivers erroneous (i.e., qualitatively wrong) results involving spurious binding.

VASP on a GPU: Application to exact-exchange calculations of the stability of elemental boron

General purpose graphical processing units (GPUʼs) offer high processing speeds for certain classes of highly parallelizable computations, such as matrix operations and Fourier transforms, that lie at the heart of first-principles electronic structure calculations. Inclusion of exact-exchange increases the cost of density functional theory by orders of magnitude, motivating the use of GPUʼs. Porting the widely used electronic density functional code VASP to run on a GPU results in a 5–20 fold performance boost of exact-exchange compared with a traditional CPU. We analyze performance bottlenecks and discuss classes of problems that will benefit from the GPU. As an illustration of the capabilities of this implementation, we calculate the lattice stability α- and β-rhombohedral boron structures utilizing exact-exchange. Our results confirm the energetic preference for symmetry-breaking partial occupation of the β-rhombohedral structure at low temperatures, but does not resolve the stability of α relative to β.

Local Hybrid Divide-and-Conquer Method for the Computation of Medium and Large Molecules.

A local hybrid divide-and-conquer method (LHDC) which combines the high accuracy of sophisticated wave function theory (WFT) methods and the low cost of density functional theory (DFT) has been proposed for computational studies of medium and large molecules. In the method, a large system is divided into small subsystems for which the coefficients of the exchange functional in a hybrid functional are first optimized according to the energy calculated by an accurate WFT method. The hybrid coefficients are then used to evaluate the energy of the whole system. The method not only can reproduce the total energies of the chosen WFT method in good accuracy but also provides electronic structure information for the entire system.