Lowering of the complexity of quantum chemistry methods by choice of representation

The complexity of the standard hierarchy of quantum chemistry methods is not invariant to the choice of representation. This work explores how the scaling of common quantum chemistry methods can be reduced using real-space, momentum-space, and time-dependent intermediate representations without introducing approximations. We find the scalings of exact Gaussian basis Hartree--Fock theory, second-order M{\o}ller-Plesset perturbation theory, and coupled cluster theory (specifically, linearized coupled cluster doubles and the distinguishable cluster approximation with doubles) to be $\mathcal{O}(N^3)$, $\mathcal{O}(N^3)$, and $\mathcal{O}(N^5)$ respectively, where $N$ denotes system size. These scalings are not asymptotic and hold over all ranges of $N$

Exploring the limit of accuracy for density functionals based on the generalized gradient approximation: Local, global hybrid, and range-separated hybrid functionals with and without dispersion corrections

The limit of accuracy for semi-empirical generalized gradient approximation (GGA) density functionals is explored by parameterizing a variety of local, global hybrid, and range-separated hybrid functionals. The training methodology employed differs from conventional approaches in 2 main ways: (1) Instead of uniformly truncating the exchange, same-spin correlation, and opposite-spin correlation functional inhomogeneity correction factors, all possible fits up to fourth order are considered, and (2) Instead of selecting the optimal functionals based solely on their training set performance, the fits are validated on an independent test set and ranked based on their overall performance on the training and test sets. The 3 different methods of accounting for exchange are trained both with and without dispersion corrections (DFT-D2 and VV10), resulting in a total of 491 508 candidate functionals. For each of the 9 functional classes considered, the results illustrate the trade-off between improved training set performance and diminished transferability. Since all 491 508 functionals are uniformly trained and tested, this methodology allows the relative strengths of each type of functional to be consistently compared and contrasted. The range-separated hybrid GGA functional paired with the VV10 nonlocal correlation functional emerges as the most accurate form for the present training and test sets, which span thermochemical energy differences, reaction barriers, and intermolecular interactions involving lighter main group elements

Self-consistent implementation of meta-GGA functionals for the ONETEP linear-scaling electronic structure package

Accurate and computationally efficient exchange-correlation functionals are critical to the successful application of linear-scaling density functional theory (DFT). Local and semi-local functionals of the density are naturally compatible with linear-scaling approaches, having a general form which assumes the locality of electronic interactions and which can be efficiently evaluated by numerical quadrature. Presently, the most sophisticated and flexible semi-local functionals are members of the meta-generalized-gradient approximation (meta-GGA) family, and depend upon the kinetic energy density, tau, in addition to the charge density and its gradient. In order to extend the theoretical and computational advantages of tau-dependent meta-GGA functionals to large-scale DFT calculations on thousands of atoms, we have implemented support for tau-dependent meta-GGA functionals in the ONETEP program. In this paper we lay out the theoretical innovations necessary to implement tau-dependent meta-GGA functionals within ONETEP's linear-scaling formalism. We present expressions for the gradient of the tau-dependent exchange-correlation energy, necessary for direct energy minimization. We also derive the forms of the tau-dependent exchange-correlation potential and kinetic energy density in terms of the strictly localized, self-consistently optimized orbitals used by ONETEP. To validate the numerical accuracy of our self-consistent meta-GGA implementation, we performed calculations using the B97M-V and PKZB meta-GGAs on a variety of small molecules. Using only a minimal basis set of self-consistently optimized local orbitals, we obtain energies in excellent agreement with large basis set calculations performed using other codes. Finally, to establish the linear-scaling computational cost and applicability of our approach to large-scale calculations, we present the outcome of self-consistent meta-GGA calculations on amyloid fibrils of increasing size, up to tens of thousands of atoms

Assessment of Density Functional Theory in Predicting Interaction Energies Between Water and Polycyclic Aromatic Hydrocarbons: From Water on Benzene to Water on Graphene

The interactions of water with polycyclic aromatic hydrocarbons, from benzene to graphene, are investigated using various exchange-correlation functionals selected across the hierarchy of density functional theory (DFT) approximations. The accuracy of the different functionals is assessed through comparisons with random phase approximation (RPA) and coupled-cluster with single, double, and perturbative triple excitations [CCSD(T)] calculations. Diffusion Monte Carlo (DMC) data reported in the literature are also used for comparison. Relatively large variations are found in interaction energies predicted by different DFT models, with GGA functionals underestimating the interaction strength for configurations with the water oxygen pointing toward the aromatic molecules. The meta-GGA B97M-rV and range-separated hybrid, meta-GGA ωB97M-V functionals provide nearly quantitative agreement with CCSD(T) values for the water–benzene, water–coronene, and water–circumcoronene dimers, while RPA and DMC predict interaction energies that differ by up to ∼1 kcal/mol and ∼0.4 kcal/mol from the corresponding CCSD(T) values, respectively. Similar trends among GGA, meta-GGA, and hybrid functionals are observed for larger polycyclic aromatic hydrocarbons. By performing absolutely localized molecular orbital energy decomposition analyses (ALMO-EDA), it is found that, independently of the number of carbon atoms and exchange-correlation functional, the dominant contributions to the interaction energies between water and polycyclic aromatic hydrocarbon molecules are the electrostatic and dispersion terms while polarization and charge transfer effects are negligibly small. Calculations carried out with GGA and meta-GGA functionals indicate that, as the number of carbon atoms increases, the interaction energies slowly converge to the corresponding values obtained for an infinite graphene sheet

Novel algorithms and high-performance cloud computing enable efficient fully quantum mechanical protein-ligand scoring

Ranking the binding of small molecules to protein receptors through physics-based computation remains challenging. Though inroads have been made using free energy methods, these fail when the underlying classical mechanical force fields are insufficient. In principle, a more accurate approach is provided by quantum mechanical density functional theory (DFT) scoring, but even with approximations, this has yet to become practical on drug discovery-relevant timescales and resources. Here, we describe how to overcome this barrier using algorithms for DFT calculations that scale on widely available cloud architectures, enabling full density functional theory, without approximations, to be applied to protein-ligand complexes with approximately 2500 atoms in tens of minutes. Applying this to a realistic example of 22 ligands binding to MCL1 reveals that density functional scoring outperforms classical free energy perturbation theory for this system. This raises the possibility of broadly applying fully quantum mechanical scoring to real-world drug discovery pipelines

Novel algorithms and high-performance cloud computing enable efficient fully quantum mechanical protein-ligand scoring

Ranking the binding of small molecules to protein receptors through physics-based computation remains challenging. Though inroads have been made using free energy methods, these fail when the underlying classical mechanical force fields are insufficient. In principle, a more accurate approach is provided by quantum mechanical density functional theory (DFT) scoring, but even with approximations, this has yet to become practical on drug discovery-relevant timescales and resources. Here, we describe how to overcome this barrier using algorithms for DFT calculations that scale on widely available cloud architectures, enabling full density functional theory, without approximations, to be applied to protein-ligand complexes with approximately 2500 atoms in tens of minutes. Applying this to a realistic example of 22 ligands binding to MCL1 reveals that density functional scoring outperforms classical free energy perturbation theory for this system. This raises the possibility of broadly applying fully quantum mechanical scoring to real-world drug discovery pipelines.Comment: 15 pages, 5 figures, 1 tabl

Assessment of Density Functional Theory in Predicting Interaction Energies Between Water and Polycyclic Aromatic Hydrocarbons: From Water on Benzene to Water on Graphene

The interactions of water with polycyclic aromatic hydrocarbons, from benzene to graphene, are investigated using various exchange-correlation functionals selected across the hierarchy of density functional theory (DFT) approximations. The accuracy of the different functionals is assessed through comparisons with random phase approximation (RPA) and coupled-cluster with single, double, and perturbative triple excitations [CCSD(T)] calculations. Diffusion Monte Carlo (DMC) data reported in the literature are also used for comparison. Relatively large variations are found in interaction energies predicted by different DFT models, with GGA functionals underestimating the interaction strength for configurations with the water oxygen pointing toward the aromatic molecules. The meta-GGA B97M-rV and range-separated hybrid, meta-GGA ωB97M-V functionals provide nearly quantitative agreement with CCSD(T) values for the water–benzene, water–coronene, and water–circumcoronene dimers, while RPA and DMC predict interaction energies that differ by up to ∼1 kcal/mol and ∼0.4 kcal/mol from the corresponding CCSD(T) values, respectively. Similar trends among GGA, meta-GGA, and hybrid functionals are observed for larger polycyclic aromatic hydrocarbons. By performing absolutely localized molecular orbital energy decomposition analyses (ALMO-EDA), it is found that, independently of the number of carbon atoms and exchange-correlation functional, the dominant contributions to the interaction energies between water and polycyclic aromatic hydrocarbon molecules are the electrostatic and dispersion terms while polarization and charge transfer effects are negligibly small. Calculations carried out with GGA and meta-GGA functionals indicate that, as the number of carbon atoms increases, the interaction energies slowly converge to the corresponding values obtained for an infinite graphene sheet

Approaching the basis set limit for DFT calculations using an environment-adapted minimal basis with perturbation theory: formulation, proof of concept, and a pilot implementation

Recently developed density functionals have good accuracy for both thermochemistry (TC) and non-covalent interactions (NC) if very large atomic orbital basis sets are used. To approach the basis set limit with potentially lower computational cost, a new self-consistent field (SCF) scheme is presented that employs minimal adaptive basis (MAB) functions. The MAB functions are optimized on each atomic site by minimizing a surrogate function. High accuracy is obtained by applying a perturbative correction (PC) to the MAB calculation, similar to dual basis approaches. Compared to exact SCF results, using this MAB-SCF?(PC) approach with the same large target basis set produces <0.15 kcal/mol root-mean-square deviations for most of the tested TC datasets, and <0.1 kcal/mol for most of the NC datasets. The performance of density functionals near the basis set limit can be even better reproduced. With further improvement to its implementation, MAB-SCF?(PC) is a promising lower-cost substitute for conventional large-basis calculations as a method to approach the basis set limit of modern density functionals