Reference-Quality Free Energy Barriers in Catalysis from Machine Learning Thermodynamic Perturbation Theory.

For the first time, we report calculations of the free energies of activation of cracking and isomerization reactions of alkenes that combine several different electronic structure methods with molecular dynamics simulations. We demonstrate that the use of a high level of theory (here Random Phase Approximation-RPA) is necessary to bridge the gap between experimental and computed values. These transformations, catalyzed by zeolites and proceeding via cationic intermediates and transition states, are building blocks of many chemical transformations for valorization of long chain paraffins originating, e.g., from plastic waste, vegetable oils, Fischer-Tropsch waxes or crude oils. Compared with the free energy barriers computed at the PBE+D2 production level of theory via constrained ab initio molecular dynamics, the barriers computed at the RPA level by the application of Machine Learning thermodynamic Perturbation Theory (MLPT) show a significant decrease for isomerization reaction and an increase of a similar magnitude for cracking, yielding an unprecedented agreement with the results obtained by experiments and kinetic modeling.

Hybrid localized graph kernel for machine learning energy-related properties of molecules and solids.

Nowadays, the coupling of electronic structure and machine learning techniques serves as a powerful tool to predict chemical and physical properties of a broad range of systems. With the aim of improving the accuracy of predictions, a large number of representations for molecules and solids for machine learning applications has been developed. In this work we propose a novel descriptor based on the notion of molecular graph. While graphs are largely employed in classification problems in cheminformatics or bioinformatics, they are not often used in regression problem, especially of energy-related properties. Our method is based on a local decomposition of atomic environments and on the hybridization of two kernel functions: a graph kernel contribution that describes the chemical pattern and a Coulomb label contribution that encodes finer details of the local geometry. The accuracy of this new kernel method in energy predictions of molecular and condensed phase systems is demonstrated by considering the popular QM7 and BA10 datasets. These examples show that the hybrid localized graph kernel outperforms traditional approaches such as, for example, the smooth overlap of atomic positions and the Coulomb matrices.

Self-Consistent Potential Correction for Charged Periodic Systems.

Supercell models are often used to calculate the electronic structure of local deviations from the ideal periodicity in the bulk or on the surface of a crystal or in wires. When the defect or adsorbent is charged, a jellium counter charge is applied to maintain overall neutrality, but the interaction of the artificially repeated charges has to be corrected, both in the total energy and in the one-electron eigenvalues and eigenstates. This becomes paramount in slab or wire calculations, where the jellium counter charge may induce spurious states in the vacuum. We present here a self-consistent potential correction scheme and provide successful tests of it for bulk and slab calculations.

Establishing the accuracy of density functional approaches for the description of noncovalent interactions in ionic liquids.

We test a number of dispersion corrected versatile Generalized Gradient Approximation (GGA) and meta-GGA functionals for their ability to predict the interactions of ionic liquids, and show that most can achieve energies within 1 kcal mol-1 of benchmarks. This compares favorably with an accurate dispersion corrected hybrid, ωB97X-V. Our tests also reveal that PBE (Perdew-Burke-Ernzerhof GGA) calculations using the plane-wave projector augmented wave method and Gaussian Type Orbitals (GTOs) differ by less than 0.6 kJ mol-1 for ionic liquids, despite ions being difficult to evaluate in periodic cells - thus revealing that GTO benchmarks may be used also for plane-wave codes. Finally, the relatively high success of explicit van der Waals density functionals, compared to elemental and ionic dispersion models, suggests that improvements are required for low-cost dispersion correction models of ions.

Establishing the accuracy of density functional approaches for the description of noncovalent interactions in biomolecules.

Biomolecules have complex structures, and noncovalent interactions are crucial to determine their conformations and functionalities. It is therefore critical to be able to describe them in an accurate but efficient manner in these systems. In this context density functional theory (DFT) could provide a powerful tool to simulate biological matter either directly for relatively simple systems or coupled with classical simulations like the QM/MM (quantum mechanics/molecular mechanics) approach. Additionally, DFT could play a fundamental role to fit the parameters of classical force fields or to train machine learning potentials to perform large scale molecular dynamics simulations of biological systems. Yet, local or semi-local approximations used in DFT cannot describe van der Waals (vdW) interactions, one of the essential noncovalent interactions in biomolecules, since they lack a proper description of long range correlation effects. However, many efficient and reasonably accurate methods are now available for the description of van der Waals interactions within DFT. In this work, we establish the accuracy of several state-of-the-art vdW-aware functionals by considering 275 biomolecules including interacting DNA and RNA bases, peptides and biological inhibitors and compare our results for the energy with highly accurate wavefunction based calculations. Most methods considered here can achieve close to predictive accuracy. In particular, the non-local vdW-DF2 functional is revealed to be the best performer for biomolecules, while among the vdW-corrected DFT methods, uMBD is also recommended as a less accurate but faster alternative.

Bathochromic Shift in the UV-Visible Absorption Spectra of Phenols at Ice Surfaces: Insights from First-Principles Calculations.

Some organic pollutants in snowpacks undergo faster photodegradation than in solution. One possible explanation for such effect is that their UV-visible absorption spectra are shifted toward lower energy when the molecules are adsorbed at the air-ice interface. However, such bathochromic shift is difficult to measure experimentally. Here, we employ a multiscale/multimodel approach that combines classical and first-principles molecular dynamics, quantum chemical methods, and statistical learning to compute the light absorption spectra of two phenolic molecules in different solvation environments at the relevant thermodynamic conditions. Our calculations provide an accurate estimate of the bathochromic shift of the lowest-energy UV-visible absorption band when these molecules are adsorbed at the air-ice interface, and they shed light into its molecular origin.

Benchmarking several van der Waals dispersion approaches for the description of intermolecular interactions.

Seven methods, including three van der Waals density functionals (vdW-DFs) and four different variants of the Tkatchenko-Scheffler (TS) methods, are tested on the A24, L7, and Taylor et al.'s "blind" test sets. It is found that for these systems, the vdW-DFs perform better that the TS methods. In particular, the vdW-DF-cx functional gives binding energies that are the closest to the reference values, while the many-body correction of TS does not always lead to an improvement in the description of molecular systems. In light of these results, several directions for further improvements to describe van der Waals interactions are discussed.

Communication: A novel implementation to compute MP2 correlation energies without basis set superposition errors and complete basis set extrapolation.

By using a formulation based on the dynamical polarizability, we propose a novel implementation of second-order Møller-Plesset perturbation (MP2) theory within a plane wave (PW) basis set. Because of the intrinsic properties of PWs, this method is not affected by basis set superposition errors. Additionally, results are converged without relying on complete basis set extrapolation techniques; this is achieved by using the eigenvectors of the static polarizability as an auxiliary basis set to compactly and accurately represent the response functions involved in the MP2 equations. Summations over the large number of virtual states are avoided by using a formalism inspired by density functional perturbation theory, and the Lanczos algorithm is used to include dynamical effects. To demonstrate this method, applications to three weakly interacting dimers are presented.

Improving the accuracy of ground-state correlation energies within a plane-wave basis set: The electron-hole exchange kernel.

A new formalism was recently proposed to improve random phase approximation (RPA) correlation energies by including approximate exchange effects [B. Mussard et al., J. Chem. Theory Comput. 12, 2191 (2016)]. Within this framework, by keeping only the electron-hole contributions to the exchange kernel, two approximations can be obtained: An adiabatic connection analog of the second order screened exchange (AC-SOSEX) and an approximate electron-hole time-dependent Hartree-Fock (eh-TDHF). Here we show how this formalism is suitable for an efficient implementation within the plane-wave basis set. The response functions involved in the AC-SOSEX and eh-TDHF equations can indeed be compactly represented by an auxiliary basis set obtained from the diagonalization of an approximate dielectric matrix. Additionally, the explicit calculation of unoccupied states can be avoided by using density functional perturbation theory techniques and the matrix elements of dynamical response functions can be efficiently computed by applying the Lanczos algorithm. As shown by several applications to reaction energies and weakly bound dimers, the inclusion of the electron-hole kernel significantly improves the accuracy of ground-state correlation energies with respect to RPA and semi-local functionals.

Random-phase approximation correlation energies from Lanczos chains and an optimal basis set: theory and applications to the benzene dimer.

A new ab initio approach is introduced to compute the correlation energy within the adiabatic connection fluctuation dissipation theorem in the random phase approximation. First, an optimally small basis set to represent the response functions is obtained by diagonalizing an approximate dielectric matrix containing the kinetic energy contribution only. Then, the Lanczos algorithm is used to compute the full dynamical dielectric matrix and the correlation energy. The convergence issues with respect to the number of empty states or the dimension of the basis set are avoided and the dynamical effects are easily kept into account. To demonstrate the accuracy and efficiency of this approach the binding curves for three different configurations of the benzene dimer are computed: T-shaped, sandwich, and slipped parallel.

Electronic excitations in light absorbers for photoelectrochemical energy conversion: first principles calculations based on many body perturbation theory.

We describe state of the art methods for the calculation of electronic excitations in solids and molecules, based on many body perturbation theory, and we discuss some applications of these methods to the study of band edges and absorption processes in representative materials used as photoelectrodes for water splitting.

Reducing the Runtime of Fault-Tolerant Quantum Simulations in Chemistry through Symmetry-Compressed Double Factorization.

Quantum phase estimation based on qubitization is the state-of-the-art fault-tolerant quantum algorithm for computing ground-state energies in chemical applications. In this context, the 1-norm of the Hamiltonian plays a fundamental role in determining the total number of required iterations and also the overall computational cost. In this work, we introduce the symmetry-compressed double factorization (SCDF) approach, which combines a CDF of the Hamiltonian with the symmetry shift technique, significantly reducing the 1-norm value. The effectiveness of this approach is demonstrated numerically by considering various benchmark systems, including the FeMoco molecule, cytochrome P450, and hydrogen chains of different sizes. To compare the efficiency of SCDF to other methods in absolute terms, we estimate Toffoli gate requirements, which dominate the execution time on fault-tolerant quantum computers. For the systems considered here, SCDF leads to a sizable reduction of the Toffoli gate count in comparison to other variants of DF or even tensor hypercontraction, which is usually regarded as the most efficient approach for qubitization.

Solving the Schrödinger Equation in the Configuration Space with Generative Machine Learning.

The configuration interaction approach provides a conceptually simple and powerful approach to solve the Schrödinger equation for realistic molecules and materials but is characterized by an unfavorable scaling, which strongly limits its practical applicability. Effectively selecting only the configurations that actually contribute to the wave function is a fundamental step toward practical applications. We propose a machine learning approach that iteratively trains a generative model to preferentially generate the important configurations. By considering molecular applications it is shown that convergence to chemical accuracy can be achieved much more rapidly with respect to random sampling or the Monte Carlo configuration interaction method. This work paves the way to a broader use of generative models to solve the electronic structure problem.

Anisotropic Excitons Reveal Local Spin Chain Directions in a van der Waals Antiferromagnet.

A long-standing pursuit in materials science is to identify suitable magnetic semiconductors for integrated information storage, processing, and transfer. Van der Waals magnets have brought forth new material candidates for this purpose. Recently, sharp exciton resonances in antiferromagnet NiPS3 have been reported to correlate with magnetic order, that is, the exciton photoluminescence intensity diminishes above the Néel temperature. Here, it is found that the polarization of maximal exciton emission rotates locally, revealing three possible spin chain directions. This discovery establishes a new understanding of the antiferromagnet order hidden in previous neutron scattering and optical experiments. Furthermore, defect-bound states are suggested as an alternative exciton formation mechanism that has yet to be explored in NiPS3 . The supporting evidence includes chemical analysis, excitation power, and thickness dependent photoluminescence and first-principles calculations. This mechanism for exciton formation is also consistent with the presence of strong phonon side bands. This study shows that anisotropic exciton photoluminescence can be used to read out local spin chain directions in antiferromagnets and realize multi-functional devices via spin-photon transduction.

A block variational procedure for the iterative diagonalization of non-Hermitian random-phase approximation matrices.

We present a technique for the iterative diagonalization of random-phase approximation (RPA) matrices, which are encountered in the framework of time-dependent density-functional theory (TDDFT) and the Bethe-Salpeter equation. The non-Hermitian character of these matrices does not permit a straightforward application of standard iterative techniques used, i.e., for the diagonalization of ground state Hamiltonians. We first introduce a new block variational principle for RPA matrices. We then develop an algorithm for the simultaneous calculation of multiple eigenvalues and eigenvectors, with convergence and stability properties similar to techniques used to iteratively diagonalize Hermitian matrices. The algorithm is validated for simple systems (Na(2) and Na(4)) and then used to compute multiple low-lying TDDFT excitation energies of the benzene molecule.

Assessing the Accuracy of Machine Learning Thermodynamic Perturbation Theory: Density Functional Theory and Beyond.

Machine learning thermodynamic perturbation theory (MLPT) is a promising approach to compute finite temperature properties when the goal is to compare several different levels of ab initio theory and/or to apply highly expensive computational methods. Indeed, starting from a production molecular dynamics trajectory, this method can estimate properties at one or more target levels of theory from only a small number of additional fixed-geometry calculations, which are used to train a machine learning model. However, as MLPT is based on thermodynamic perturbation theory (TPT), inaccuracies might arise when the starting point trajectory samples a configurational space which has a small overlap with that of the target approximations of interest. By considering case studies of molecules adsorbed in zeolites and several different density functional theory approximations, in this work we assess the accuracy of MLPT for ensemble total energies and enthalpies of adsorption. It is shown that problematic cases can be detected even without knowing reference results and that even in these situations it is possible to recover target level results within chemical accuracy by applying a machine-learning-based Monte Carlo (MLMC) resampling. Finally, on the basis of the ideas developed in this work, we assess and confirm the accuracy of recently published MLPT-based enthalpies of adsorption at the random phase approximation level, whose high computational cost would completely hinder a direct molecular dynamics simulation.

Beyond Conformational Control: Effects of Noncovalent Interactions on Molecular Electronic Properties of Conjugated Polymers.

Tuning the electronic properties of polymers is of great importance in designing highly efficient organic solar cells. Noncovalent intramolecular interactions have been often used for conformational control to enhance the planarity of polymers or molecules, which may reduce band gaps and promote charge transfer. However, it is not known if noncovalent interactions may alter the electronic properties of conjugated polymers through some mechanism other than the conformational control. Here, we studied the effects of various noncovalent interactions, including sulfur-nitrogen, sulfur-oxygen, sulfur-fluorine, oxygen-nitrogen, oxygen-fluorine, and nitrogen-fluorine, on the electronic properties of polymers with planar geometry using unconstrained and constrained density functional theory. We found that the sulfur-nitrogen intramolecular interaction may reduce the band gaps of polymers and enhance the charge transfer more obviously than other noncovalent interactions. Our findings are also consistent with the experimental data. For the first time, our study shows that the sulfur-nitrogen noncovalent interaction may further affect the electronic structure of coplanar conjugated polymers, which cannot be only explained by the enhancement of molecular planarity. Our work suggests a new mechanism to manipulate the electronic properties of polymers to design high-performance small-molecule-polymer and all-polymer solar cells.

Structure and Energetics of Dye-Sensitized NiO Interfaces in Water from Ab Initio MD and Large-Scale GW Calculations.

The energy-level alignment across solvated molecule/semiconductor interfaces is a crucial property for the correct functioning of dye-sensitized photoelectrodes, where, following the absorption of solar light, a cascade of interfacial hole/electron transfer processes has to efficiently take place. In light of the difficulty of performing X-ray photoelectron spectroscopy measurements at the molecule/solvent/metal-oxide interface, being able to accurately predict the level alignment by first-principles calculations on realistic structural models would represent an important step toward the optimization of the device. In this respect, dye/NiO surfaces, employed in p-type dye-sensitized solar cells, are undoubtedly challenging for ab initio methods and, also for this reason, much less investigated than the n-type dye/TiO2 counterpart. Here, we consider the C343-sensitized NiO surface in water and combine ab initio molecular dynamics (AIMD) simulations with GW (G0W0) calculations, performed along the MD trajectory to reliably describe the structure and energetics of the interface when explicit solvation and finite temperature effects are accounted for. We show that the differential perturbative correction on the NiO and molecule states obtained at the GW level is mandatory to recover the correct (physical) interfacial energetics, allowing hole transfer from the semiconductor valence band to the highest occupied molecular orbital (HOMO) of the dye. Moreover, the calculated average driving force quantitatively agrees with the experimental estimate.

Ab initio calculations of optical absorption spectra: solution of the Bethe-Salpeter equation within density matrix perturbation theory.

We describe an ab initio approach to compute the optical absorption spectra of molecules and solids, which is suitable for the study of large systems and gives access to spectra within a wide energy range. In this approach, the quantum Liouville equation is solved iteratively within first order perturbation theory, with a Hamiltonian containing a static self-energy operator. This procedure is equivalent to solving the statically screened Bethe-Salpeter equation. Explicit calculations of single particle excited states and inversion of dielectric matrices are avoided using techniques based on density functional perturbation theory. In this way, full absorption spectra may be obtained with a computational workload comparable to ground state Hartree-Fock calculations. We present results for small molecules, for the spectra of a 1 nm Si cluster in a wide energy range (20 eV), and for a dipeptide exhibiting charge transfer excitations.

High-energy excitations in silicon nanoparticles.

We have investigated high energy excitations in approximately 1-2 nm Si nanoparticles (NPs) by ab initio time-dependent density functional calculations, focusing on the influence on excitation spectra, of surface reconstruction, surface passivation by alkyl groups, and the interaction between NPs. We have found that surface reconstruction may change excitation spectra dramatically at both low and high energies above the gap; absorption may be enhanced nonlinearly by the presence of alkyl groups, compared to that of unreconstructed, hydrogenated Si NPs, and by the interaction between NPs. Our findings can help interpret the recent experiments on multielectron generation in colloidal semiconductor NPs as well as help optimize photovoltaic applications of NPs.