*J Phys Chem Lett ; : 6946-6955, 2020 Aug 12.*

##### RESUMO

The on-the-fly generation of machine-learning force fields by active-learning schemes attracts a great deal of attention in the community of atomistic simulations. The algorithms allow the machine to self-learn an interatomic potential and construct machine-learned models on the fly during simulations. State-of-the-art query strategies allow the machine to judge whether new structures are out of the training data set or not. Only when the machine judges the necessity of updating the data set with the new structures are first-principles calculations carried out. Otherwise, the yet available machine-learned model is used to update the atomic positions. In this manner, most of the first-principles calculations are bypassed during training, and overall, simulations are accelerated by several orders of magnitude while retaining almost first-principles accuracy. In this Perspective, after describing essential components of the active-learning algorithms, we demonstrate the power of the schemes by presenting recent applications.

*J Chem Phys ; 152(23): 234102, 2020 Jun 21.*

##### RESUMO

When determining machine-learning models for inter-atomic potentials, the potential energy surface is often described as a non-linear function of descriptors representing two- and three-body atomic distribution functions. It is not obvious how the choice of the descriptors affects the efficiency of the training and the accuracy of the final machine-learned model. In this work, we formulate an efficient method to calculate descriptors that can separately represent two- and three-body atomic distribution functions, and we examine the effects of including only two- or three-body descriptors, as well as including both, in the regression model. Our study indicates that non-linear mixing of two- and three-body descriptors is essential for an efficient training and a high accuracy of the final machine-learned model. The efficiency can be further improved by weighting the two-body descriptors more strongly. We furthermore examine a sparsification of the three-body descriptors. The three-body descriptors usually provide redundant representations of the atomistic structure, and the number of descriptors can be significantly reduced without loss of accuracy by applying an automatic sparsification using a principal component analysis. Visualization of the reduced descriptors using three-body distribution functions in real-space indicates that the sparsification automatically removes the components that are less significant for describing the distribution function.

*J Phys Condens Matter ; 32(1): 015502, 2020 Jan 01.*

##### RESUMO

Recently, two nonempirical hybrid functionals, dielectric-dependent range-separated hybrid functional based on the Coulomb-attenuating method (DD-RSH-CAM) and doubly screened hybrid functional (DSH), have been suggested by Chen et al (2018 Phys. Rev. Mater. 2 073803) and Cui et al (2018 J. Phys. Chem. Lett. 9 2338), respectively. These two hybrid functionals are both based on a common model dielectric function approach, but differ in the way how to non-empirically obtain the range-separation parameter. By retaining the full short-range Fock exchange and a fraction of the long-range Fock exchange that equals the inverse of the dielectric constant, both DD-RSH-CAM and DSH turn out to perform very well in predicting the band gaps for a large variety of semiconductors and insulators. Here, we assess how these two hybrid functionals perform on challenging antiferromagnetic transition-metal monoxides MnO, FeO, CoO, and NiO by comparing them to other conventional hybrid functionals and the GW method. We find that single-shot DD0-RSH-CAM and DSH0 improve the band gaps towards experiments as compared to conventional hybrid functionals. The magnetic moments are slightly increased, but the predicted dielectric constants are decreased. The valence band density of states (DOS) predicted by DD0-RSH-CAM and DSH0 are as satisfactory as HSE03 in comparison to experimental spectra, however, the conduction band DOS are shifted to higher energies by about 2 eV compared to HSE03. Self-consistent DD-RSH-CAM and DSH deteriorate the results with a significant overestimation of band gaps.

*J Chem Phys ; 151(21): 214106, 2019 Dec 07.*

##### RESUMO

We present a method to approximate post-Hartree-Fock correlation energies by using approximate natural orbitals obtained by the random phase approximation (RPA). We demonstrate the method by applying it to the helium atom, the hydrogen and fluorine molecule, and to diamond as an example of a periodic system. For these benchmark systems, we show that RPA natural orbitals converge the MP2 correlation energy rapidly. Additionally, we calculated full configuration interaction energies for He and H2, which are in excellent agreement with the literature and experimental values. We conclude that the proposed method may serve as a compromise to reach good approximations to correlation energies at moderate computational cost, and we expect the method to be especially useful for theoretical studies on surface chemistry by providing an efficient basis to correlated wave function based methods.

*Angew Chem Int Ed Engl ; 58(50): 17964-17968, 2019 Dec 09.*

##### RESUMO

The chemical nature and aggregate state of superheavy copernicium (Cn) have been subject of speculation for many years. While strong relativistic effects render Cn chemically inert, which led Pitzer to suggest a noble-gas-like behavior in 1975, Eichler and co-workers in 2008 reported substantial interactions with a gold surface in atom-at-a-time experiments, suggesting a metallic character and a solid aggregate state. Herein, we explore the physicochemical properties of Cn by means of first-principles free-energy calculations, which confirm Pitzer's original hypothesis: With predicted melting and boiling points of 283±11â K and 340±10â K, Cn is indeed a volatile liquid and exhibits a density very similar to that of mercury. However, in stark contrast to mercury and the lighter Groupâ 12 metals, we find bulk Cn to be bound by dispersion and to exhibit a large band gap of 6.4â eV, which is consistent with a noble-gas-like character. This non-group-conforming behavior is eventually traced back to strong scalar-relativistic effects, and in the non-relativistic limit, Cn appears as a common Groupâ 12 metal.

*Phys Rev Lett ; 122(22): 225701, 2019 Jun 07.*

##### RESUMO

Realistic finite temperature simulations of matter are a formidable challenge for first principles methods. Long simulation times and large length scales are required, demanding years of computing time. Here we present an on-the-fly machine learning scheme that generates force fields automatically during molecular dynamics simulations. This opens up the required time and length scales, while retaining the distinctive chemical precision of first principles methods and minimizing the need for human intervention. The method is widely applicable to multielement complex systems. We demonstrate its predictive power on the entropy driven phase transitions of hybrid perovskites, which have never been accurately described in simulations. Using machine learned potentials, isothermal-isobaric simulations give direct insight into the underlying microscopic mechanisms. Finally, we relate the phase transition temperatures of different perovskites to the radii of the involved species, and we determine the order of the transitions in Landau theory.

*J Chem Theory Comput ; 15(5): 3223-3236, 2019 May 14.*

##### RESUMO

The random phase approximation (RPA) systematically overestimates the magnitude of the correlation energy and generally underestimates cohesive energies. This originates in part from the complete lack of exchange terms that would otherwise cancel Pauli exclusion principle violating (EPV) contributions. The uncanceled EPV contributions also manifest themselves in form of an unphysical negative pair density of spin-parallel electrons close to electron-electron coalescence. We follow considerations of many-body perturbation theory to propose an exchange correction that corrects the largest set of EPV contributions, while having the lowest possible computational complexity. The proposed method exchanges adjacent particle/hole pairs in the RPA diagrams, considerably improving the pair density of spin-parallel electrons close to coalescence in the uniform electron gas (UEG). The accuracy of the correlation energy is comparable to other variants of second-order screened exchange (SOSEX) corrections although it is slightly more accurate for the spin-polarized UEG. Its computational complexity scales as [Formula: see text] or [Formula: see text] in orbital space or real space, respectively. Its memory requirement scales as [Formula: see text].

*J Phys Chem Lett ; 10(3): 358-368, 2019 Feb 07.*

##### RESUMO

Wet carbon interfaces are ubiquitous in the natural world and exhibit anomalous properties, which could be exploited by emerging technologies. However, progress is limited by lack of understanding at the molecular level. Remarkably, even for the most fundamental system (a single water molecule interacting with graphene), there is no consensus on the nature of the interaction. We tackle this by performing an extensive set of complementary state-of-the-art computer simulations on some of the world's largest supercomputers. From this effort a consensus on the water-graphene interaction strength has been obtained. Our results have significant impact for the physical understanding, as they indicate that the interaction is weaker than predicted previously. They also pave the way for more accurate and reliable studies of liquid water at carbon interfaces.

*Phys Rev Lett ; 121(19): 195701, 2018 Nov 09.*

##### RESUMO

The melting point of silicon in the cubic diamond phase is calculated using the random phase approximation (RPA). The RPA includes exact exchange as well as an approximate treatment of local as well as nonlocal many body correlation effects of the electrons. We predict a melting temperature of about 1735 and 1640 K without and with core polarization effects, respectively. Both values are within 3% of the experimental melting temperature of 1687 K. In comparison, the commonly used gradient approximation to density functional theory predicts a melting point that is 200 K too low, and hybrid functionals overestimate the melting point by 150 K. We correlate the predicted melting point with the energy difference between cubic diamond and the beta-tin phase of silicon, establishing that this energy difference is an important benchmark for the development of approximate functionals. The current results demonstrate that the RPA can be used to predict accurate finite temperature properties and underlines the excellent predictive properties of the RPA for condensed matter.

*J Chem Phys ; 149(14): 144106, 2018 Oct 14.*

##### RESUMO

A variety of approaches are presented for the computation of atomic and molecular correlation energies based on the Bethe-Salpeter equation in the framework of the adiabatic-connection fluctuation-dissipation theorem. The performance of the approaches is assessed by computing the total energies of the atoms H-Ne and the atomization energies of the high-accuracy extrapolated ab initio thermochemistry set of small molecules as well as by determining the bond lengths and harmonic vibrational frequencies of the metal monoxides MO with M=Ca-Zn.

*J Chem Phys ; 148(6): 064103, 2018 Feb 14.*

##### RESUMO

We present an implementation and analysis of a stochastic high performance algorithm to calculate the correlation energy of three-dimensional periodic systems in second-order Møller-Plesset perturbation theory (MP2). In particular we measure the scaling behavior of the sample variance and probe whether this stochastic approach is competitive if accuracies well below 1 meV per valence orbital are required, as it is necessary for calculations of adsorption, binding, or surface energies. The algorithm is based on the Laplace transformed MP2 (LTMP2) formulation in the plane wave basis. The time-dependent Hartree-Fock orbitals, appearing in the LTMP2 formulation, are stochastically rotated in the occupied and unoccupied Hilbert space. This avoids a full summation over all combinations of occupied and unoccupied orbitals, as inspired by the work of Neuhauser, Rabani, and Baer [J. Chem. Theory Comput. 9, 24 (2013)]. Additionally, correlated sampling is introduced, accelerating the statistical convergence significantly.

*Phys Rev Lett ; 119(14): 145501, 2017 Oct 06.*

##### RESUMO

Which density functional is the "best" for structure simulations of a particular material? A concise, first principles, approach to answer this question is presented. The random phase approximation (RPA)-an accurate many body theory-is used to evaluate various density functionals. To demonstrate and verify the method, we apply it to the hybrid perovskite MAPbI_{3}, a promising new solar cell material. The evaluation is done by first creating finite temperature ensembles for small supercells using RPA molecular dynamics, and then evaluating the variance between the RPA and various approximate density functionals for these ensembles. We find that, contrary to recent suggestions, van der Waals functionals do not improve the description of the material, whereas hybrid functionals and the strongly constrained appropriately normed (SCAN) density functional yield very good agreement with the RPA. Finally, our study shows that in the room temperature tetragonal phase of MAPbI_{3}, the molecules are preferentially parallel to the shorter lattice vectors but reorientation on ps time scales is still possible.

*J Chem Theory Comput ; 13(10): 4765-4778, 2017 Oct 10.*

##### RESUMO

Hedin's scheme is solved with the inclusion of the vertex function (GWΓ) for a set of small molecules. The computational scheme allows for the consistent inclusion of the vertex both at the polarizability level and in the self-energy. A diagrammatic analysis shows that the self-energy formed with this four-point vertex does not lead to double counting of diagrams, that can be classified as direct "bubbles" and exchange diagrams. By removing the exchange diagrams from the self-energy, a simpler approximation is obtained, called GWtc-tc. Very good agreement with expensive wave function-based methods is obtained for both approximations.

*J Phys Chem Lett ; 8(17): 4113-4121, 2017 Sep 07.*

##### RESUMO

Dielectric constants of MAPbX3 (X = Br, I) in the 1 kHz-1 MHz range show strong temperature dependence near room temperature, in contrast to the nearly temperature-independent dielectric constant of CsPbBr3. This strong temperature dependence for MAPbX3 in the tetragonal phase is attributed to the MA+ dipoles rotating freely within the probing time scale. This interpretation is supported by ab initio molecular dynamics simulations on MAPbI3 that establish these dipoles as randomly oriented with a rotational relaxation time scale of â¼7 ps at 300 K. Further, we probe the intriguing possibility of transient polarization of these dipoles following a photoexcitation process with important consequences on the photovoltaic efficiency, using a photoexcitation pump and second harmonic generation efficiency as a probe with delay times spanning 100 fs-1.8 ns. The absence of a second harmonic signal at any delay time rules out the possibility of any transient ferroelectric state under photoexcitation.

*J Chem Phys ; 147(4): 044710, 2017 Jul 28.*

##### RESUMO

Molecular adsorption on surfaces plays an important part in catalysis, corrosion, desalination, and various other processes that are relevant to industry and in nature. As a complement to experiments, accurate adsorption energies can be obtained using various sophisticated electronic structure methods that can now be applied to periodic systems. The adsorption energy of water on boron nitride substrates, going from zero to 2-dimensional periodicity, is particularly interesting as it calls for an accurate treatment of polarizable electrostatics and dispersion interactions, as well as posing a practical challenge to experiments and electronic structure methods. Here, we present reference adsorption energies, static polarizabilities, and dynamic polarizabilities, for water on BN substrates of varying size and dimension. Adsorption energies are computed with coupled cluster theory, fixed-node quantum Monte Carlo (FNQMC), the random phase approximation, and second order Møller-Plesset theory. These wavefunction based correlated methods are found to agree in molecular as well as periodic systems. The best estimate of the water/h-BN adsorption energy is -107±7 meV from FNQMC. In addition, the water adsorption energy on the BN substrates could be expected to grow monotonically with the size of the substrate due to increased dispersion interactions, but interestingly, this is not the case here. This peculiar finding is explained using the static polarizabilities and molecular dispersion coefficients of the systems, as computed from time-dependent density functional theory (DFT). Dynamic as well as static polarizabilities are found to be highly anisotropic in these systems. In addition, the many-body dispersion method in DFT emerges as a particularly useful estimation of finite size effects for other expensive, many-body wavefunction based methods.

*J Chem Phys ; 146(10): 104101, 2017 Mar 14.*

##### RESUMO

We present a low-complexity algorithm to calculate the correlation energy of periodic systems in second-order Møller-Plesset (MP2) perturbation theory. In contrast to previous approximation-free MP2 codes, our implementation possesses a quartic scaling, O(N4), with respect to the system size N and offers an almost ideal parallelization efficiency. The general issue that the correlation energy converges slowly with the number of basis functions is eased by an internal basis set extrapolation. The key concept to reduce the scaling is to eliminate all summations over virtual orbitals which can be elegantly achieved in the Laplace transformed MP2 formulation using plane wave basis sets and fast Fourier transforms. Analogously, this approach could allow us to calculate second order screened exchange as well as particle-hole ladder diagrams with a similar low complexity. Hence, the presented method can be considered as a step towards systematically improved correlation energies.

*Phys Rev Lett ; 118(10): 106403, 2017 Mar 10.*

##### RESUMO

We discuss that in the random phase approximation (RPA) the first derivative of the energy with respect to the Green's function is the self-energy in the GW approximation. This relationship allows us to derive compact equations for the RPA interatomic forces. We also show that position dependent overlap operators are elegantly incorporated in the present framework. The RPA force equations have been implemented in the projector augmented wave formalism, and we present illustrative applications, including ab initio molecular dynamics simulations, the calculation of phonon dispersion relations for diamond and graphite, as well as structural relaxations for water on boron nitride. The present derivation establishes a concise framework for forces within perturbative approaches and is also applicable to more involved approximations for the correlation energy.

*J Chem Phys ; 146(6): 064110, 2017 Feb 14.*

##### RESUMO

Linear optical properties can be calculated by solving the time-dependent density functional theory equations. Linearization of the equation of motion around the ground state orbitals results in the so-called Casida equation, which is formally very similar to the Bethe-Salpeter equation. Alternatively one can determine the spectral functions by applying an infinitely short electric field in time and then following the evolution of the electron orbitals and the evolution of the dipole moments. The long wavelength response function is then given by the Fourier transformation of the evolution of the dipole moments in time. In this work, we compare the results and performance of these two approaches for the projector augmented wave method. To allow for large time steps and still rely on a simple difference scheme to solve the differential equation, we correct for the errors in the frequency domain, using a simple analytic equation. In general, we find that both approaches yield virtually indistinguishable results. For standard density functionals, the time evolution approach is, with respect to the computational performance, clearly superior compared to the solution of the Casida equation. However, for functionals including nonlocal exchange, the direct solution of the Casida equation is usually much more efficient, even though it scales less beneficial with the system size. We relate this to the large computational prefactors in evaluating the nonlocal exchange, which renders the time evolution algorithm fairly inefficient.

*J Chem Theory Comput ; 13(2): 635-648, 2017 Feb 14.*

##### RESUMO

In a recent work, van Setten and co-workers have presented a carefully converged G0W0 study of 100 closed shell molecules [ J. Chem. Theory Comput. 2015 , 11 , 5665 - 5687 ]. For two different codes they found excellent agreement to within a few 10 meV if identical Gaussian basis sets were used. We inspect the same set of molecules using the projector augmented wave method and the Vienna ab initio simulation package (VASP). For the ionization potential, the basis set extrapolated plane wave results agree very well with the Gaussian basis sets, often reaching better than 50 meV agreement. In order to achieve this agreement, we correct for finite basis set errors as well as errors introduced by periodically repeated images. For positive electron affinities differences between Gaussian basis sets and VASP are slightly larger. We attribute this to larger basis set extrapolation errors for the Gaussian basis sets. For quasi particle (QP) resonances above the vacuum level, differences between VASP and Gaussian basis sets are, however, found to be substantial. This is tentatively explained by insufficient basis set convergence of the Gaussian type orbital calculations as exemplified for selected test cases.