Optimizing Jastrow factors for the transcorrelated method.

We investigate the optimization of flexible tailored real-space Jastrow factors for use in the transcorrelated (TC) method in combination with highly accurate quantum chemistry methods, such as initiator full configuration interaction quantum Monte Carlo (FCIQMC). Jastrow factors obtained by minimizing the variance of the TC reference energy are found to yield better, more consistent results than those obtained by minimizing the variational energy. We compute all-electron atomization energies for the challenging first-row molecules C2, CN, N2, and O2 and find that the TC method yields chemically accurate results using only the cc-pVTZ basis set, roughly matching the accuracy of non-TC calculations with the much larger cc-pV5Z basis set.

Response to Comment on "Pushing the frontiers of density functionals by solving the fractional electron problem".

Gerasimov . claim that the ability of DM21 to respect fractional charge (FC) and fractional spin (FS) conditions outside of the training set has not been demonstrated in our paper. This is based on (i) asserting that the training set has a ~50% overlap with our bond-breaking benchmark (BBB) and (ii) questioning the validity and accuracy of our other generalization examples.

Potential pitfalls in analysing a SARS-CoV-2 RT-PCR assay and how to standardise data interpretation.

The emergence of SARS-CoV-2 in December 2019 lead to the rapid implementation of assays for virus detection, with real-time RT-PCR arguably considered the gold-standard. In our laboratory Altona RealStar SARS-Cov-2 RT-PCR kits are used with Applied Biosystems QuantStudio 7 Flex thermocyclers. Real-time PCR data interpretation is potentially complex and time-consuming, particularly for SARS-CoV-2, where the laboratory handles up to 2000 samples each day.

Pushing the frontiers of density functionals by solving the fractional electron problem.

Density functional theory describes matter at the quantum level, but all popular approximations suffer from systematic errors that arise from the violation of mathematical properties of the exact functional. We overcame this fundamental limitation by training a neural network on molecular data and on fictitious systems with fractional charge and spin. The resulting functional, DM21 (DeepMind 21), correctly describes typical examples of artificial charge delocalization and strong correlation and performs better than traditional functionals on thorough benchmarks for main-group atoms and molecules.

Transcorrelated coupled cluster methods.

Transcorrelated coupled cluster and distinguishable cluster methods are presented. The Hamiltonian is similarity transformed with a Jastrow factor in the first quantization, which results in up to three-body integrals. The coupled cluster with singles and doubles equations on this transformed Hamiltonian are formulated and implemented.

Binding curve of the beryllium dimer using similarity-transformed FCIQMC: Spectroscopic accuracy with triple-zeta basis sets.

We demonstrate how similarity-transformed full configuration interaction quantum Monte Carlo (FCIQMC) based on the transcorrelated Hamiltonian can be applied to make highly accurate predictions for the binding curve of the beryllium dimer, marking the first case study of a molecular system with this method. In this context, the non-Hermitian transcorrelated Hamiltonian, resulting from a similarity transformation with a Jastrow factor, serves the purpose to effectively address dynamic correlation beyond the used basis set and thus allows for obtaining energies close to the complete basis set limit from FCIQMC already with moderate basis sets and computational effort. Building on results from other explicitly correlated methods, we discuss the role of the Jastrow factor and its functional form, as well as potential sources for size consistency errors, and arrive at Jastrow forms that allow for high accuracy calculations of the vibrational spectrum of the beryllium dimer.

COVID-19 in multiple sclerosis and neuromyelitis optica spectrum disorder patients in Latin America: COVID-19 in MS and NMOSD patients in LATAM.

Background: There is no data regarding COVID-19 in Multiple Sclerosis (MS) and neuromyelitis optica spectrum disorder (NMOSD) patients in Latin America.

Objective: The objective of this study was to describe the clinical characteristics and outcomes of patients included in RELACOEM, a LATAM registry of MS and NMOSD patients infected with COVID-19.

Methods: RELACOEM is a longitudinal, strictly observational registry of MS and NMOSD patients who suffer COVID-19 and Dengue in LATAM.

Exact Density Functional Obtained via the Levy Constrained Search.

A stochastic minimization method for a real-space wave function, Ψ(r, r...

Fermionic Statistics in the Strongly Correlated Limit of Density Functional Theory.

Exact pieces of information on the adiabatic connection integrand, W[ρ], which allows evaluation of the exchange-correlation energy of Kohn-Sham density functional theory, can be extracted from the leading terms in the strong coupling limit (λ → ∞, where λ is the strength of the electron-electron interaction). In this work, we first compare the theoretical prediction for the two leading terms in the strong coupling limit with data obtained via numerical implementation of the exact Levy functional in the simple case of two electrons confined in one dimension, confirming the asymptotic exactness of these two terms. We then carry out a first study on the incorporation of the Fermionic statistics at large coupling λ, both numerical and theoretical, confirming that spin effects enter at orders ∼e.

On the accuracy of density functional theory and wave function methods for calculating vertical ionization energies.

The best practice in computational methods for determining vertical ionization energies (VIEs) is assessed, via reference to experimentally determined VIEs that are corroborated by highly accurate coupled-cluster calculations. These reference values are used to benchmark the performance of density functional theory (DFT) and wave function methods: Hartree-Fock theory, second-order Møller-Plesset perturbation theory, and Electron Propagator Theory (EPT). The core test set consists of 147 small molecules.

Local scaling correction for reducing delocalization error in density functional approximations.

Delocalization error is one of the most fundamental and dominant errors that plagues presently used density functional approximations. It is responsible for a large class of problems in the density functional theory calculations. For an effective and universal alleviation of the delocalization error, we develop a local scaling correction scheme by imposing the Perdew-Parr-Levy- Balduz linearity condition to local regions of a system.

Dramatic changes in electronic structure revealed by fractionally charged nuclei.

Discontinuous changes in the electronic structure upon infinitesimal changes to the Hamiltonian are demonstrated. These are revealed in one and two electron molecular systems by full configuration interaction (FCI) calculations when the realm of the nuclear charge is extended to be fractional. FCI electron densities in these systems show dramatic changes in real space and illustrate the transfer, hopping, and removal of electrons.

Qualitative breakdown of the unrestricted Hartree-Fock energy.

The stretching of closed-shell molecules is a qualitative problem for restricted Hartree-Fock that is usually circumvented by the use of unrestricted Hartree-Fock (UHF). UHF is well known to break the spin symmetry at the Coulson-Fischer point, leading to a discontinuous derivative in the potential energy surface and incorrect spin density. However, this is generally not considered as a major drawback.

The derivative discontinuity of the exchange-correlation functional.

The derivative discontinuity is a key concept in electronic structure theory in general and density functional theory in particular. The electronic energy of a quantum system exhibits derivative discontinuities with respect to different degrees of freedom that are a consequence of the integer nature of electrons. The classical understanding refers to the derivative discontinuity of the total energy as a function of the total number of electrons (N), but it can also manifest at constant N.

Extension of many-body theory and approximate density functionals to fractional charges and fractional spins.

The exact conditions for density functionals and density matrix functionals in terms of fractional charges and fractional spins are known, and their violation in commonly used functionals has been shown to be the root of many major failures in practical applications. However, approximate functionals are designed for physical systems with integer charges and spins, not in terms of the fractional variables. Here we develop a general framework for extending approximate density functionals and many-electron theory to fractional-charge and fractional-spin systems.

Derivative discontinuity, bandgap and lowest unoccupied molecular orbital in density functional theory.

The conventional analysis of Perdew and Levy, and Sham and Schlüter shows that the functional derivative discontinuity of the exchange-correlation density functional plays a critical role in the correct prediction of bandgaps, or the chemical hardness. In a recent work by the present authors, explicit expressions for bandgap prediction with all common types of exchange-correlation functionals have been derived without invoking the concept of exchange-correlation energy functional derivative discontinuity at all. We here analyze the two approaches and establish their connection and difference.

Analytical evaluation of Fukui functions and real-space linear response function.

Many useful concepts developed within density functional theory provide much insight for the understanding and prediction of chemical reactivity, one of the main aims in the field of conceptual density functional theory. While approximate evaluations of such concepts exist, the analytical and efficient evaluation is, however, challenging, because such concepts are usually expressed in terms of functional derivatives with respect to the electron density, or partial derivatives with respect to the number of electrons, complicating the connection to the computational variables of the Kohn-Sham one-electron orbitals. Only recently, the analytical expressions for the chemical potential, one of the key concepts, have been derived by Cohen, Mori-Sánchez, and Yang, based on the potential functional theory formalism.

Improving band gap prediction in density functional theory from molecules to solids.

A novel nonempirical scaling correction method is developed to tackle the challenge of band gap prediction in density functional theory. For finite systems the scaling correction largely restores the straight-line behavior of electronic energy at fractional electron numbers. The scaling correction can be generally applied to a variety of mainstream density functional approximations, leading to significant improvement in the band gap prediction.

Second-Order Perturbation Theory with Fractional Charges and Fractional Spins.

In this work the behavior of MP2 for fractional occupations is investigated. The consideration of fractional charge behavior gives a simple derivation of an expression for the chemical potential (or the derivative of energy with respect to the number of electrons) of MP2. A generalized optimized effective potential formalism (OEP) has been developed in which the OEP is a nonlocal potential, which can be applied to explicit functionals of the orbitals and eigenvalues and also facilitates the evaluation of the chemical potential.

Discontinuous nature of the exchange-correlation functional in strongly correlated systems.

Standard approximations for the exchange-correlation functional have been found to give big errors for the linearity condition of fractional charges, leading to delocalization error, and the constancy condition of fractional spins, leading to static correlation error. These two conditions are now unified and extended to states with both fractional charge and fractional spin to give a much more stringent condition: the exact energy functional is a plane, linear along the fractional charge coordinate and constant along the fractional spin coordinate with a line of discontinuity at the integer. Violation of this condition underlies the failure of all known approximate functionals to describe the gaps in strongly correlated systems.

Delocalization errors in density functionals and implications for main-group thermochemistry.

The difficulty of approximate density functionals in describing the energetics of Diels-Alder reactions and dimerization of aluminum complexes is analyzed. Both of these reaction classes involve formation of cyclic or bicyclic products, which are found to be underbound by the majority of functionals considered. We present a consistent view of these results from the perspective of delocalization error.

A pseudobond parametrization for improved electrostatics in quantum mechanical/molecular mechanical simulations of enzymes.

The pseudobond method is used in quantum mechanical/molecular mechanical (QM/MM) simulations in which a covalent bond connects the quantum mechanical and classical subsystems. In this method, the molecular mechanical boundary atom is replaced by a special quantum mechanical atom with one free valence that forms a bond with the rest of the quantum mechanical subsystem. This boundary atom is modified through the use of a parametrized effective core potential and basis set.