Thorben Petersen

The Journal of Chemical Physics, Volume 154, Issue 1, January 2021.
We present an embedding approach to treat local electron correlation effects in periodic environments. In a single consistent framework, our plane wave based scheme embeds a local high-level correlation calculation [here, Coupled Cluster (CC) theory], employing localized orbitals, into a low-level correlation calculation [here, the direct Random Phase Approximation (RPA)]. This choice allows for an accurate and efficient treatment of long-range dispersion effects. Accelerated convergence with respect to the local fragment size can be observed if the low-level and high-level long-range dispersions are quantitatively similar, as is the case for CC in RPA. To demonstrate the capabilities of the introduced embedding approach, we calculate adsorption energies of molecules on a surface and in a chabazite crystal cage, as well as the formation energy of a lattice impurity in a solid at the level of highly accurate many-electron perturbation theories. The absorption energy of a methane molecule in a zeolite chabazite is converged with an error well below 20 meV at the CC level. As our largest periodic benchmark system, we apply our scheme to the adsorption of a water molecule on titania in a supercell containing more than 1000 electrons.

The Journal of Chemical Physics, Volume EISC2020, Issue 1, December 2020.
Oxygen vacancies are ubiquitous in TiO2 and play key roles in catalysis and magnetism applications. Despite being extensively investigated, the electronic structure of oxygen vacancies in TiO2 remains controversial both experimentally and theoretically. Here, we report a study of a neutral oxygen vacancy in TiO2 using state-of-the-art quantum chemical electronic structure methods. We find that the ground state is a color center singlet state in both the rutile and the anatase phases of TiO2. Specifically, embedded coupled cluster with singles, doubles, and perturbative triples calculations find, for an oxygen vacancy in rutile, that the lowest triplet state energy is 0.6 eV above the singlet state, and in anatase, the triplet state energy is higher by 1.4 eV. Our study provides fresh insights into the electronic structure of the oxygen vacancy in TiO2, clarifying earlier controversies and potentially inspiring future studies of defects with correlated wave function theories.

The Journal of Chemical Physics, Volume 153, Issue 20, November 2020.
Oxygen vacancies are ubiquitous in TiO2 and play key roles in catalysis and magnetism applications. Despite being extensively investigated, the electronic structure of oxygen vacancies in TiO2 remains controversial both experimentally and theoretically. Here, we report a study of a neutral oxygen vacancy in TiO2 using state-of-the-art quantum chemical electronic structure methods. We find that the ground state is a color center singlet state in both the rutile and the anatase phases of TiO2. Specifically, embedded coupled cluster with singles, doubles, and perturbative triples calculations find, for an oxygen vacancy in rutile, that the lowest triplet state energy is 0.6 eV above the singlet state, and in anatase, the triplet state energy is higher by 1.4 eV. Our study provides fresh insights into the electronic structure of the oxygen vacancy in TiO2, clarifying earlier controversies and potentially inspiring future studies of defects with correlated wave function theories.

Author(s): Edoardo Baldini, Tania Palmieri, Adriel Dominguez, Angel Rubio, and Majed Chergui

Elucidating the carrier density at which strongly bound excitons dissociate into a plasma of uncorrelated electron-hole pairs is a central topic in the many-body physics of semiconductors. However, there is a lack of information on the high-density response of excitons absorbing in the near-to-mid u...

[Phys. Rev. Lett. 125, 116403] Published Thu Sep 10, 2020

The Journal of Chemical Physics, Volume ESS2020, Issue 1, June 2020.
In this contribution to the special software-centered issue, the ORCA program package is described. We start with a short historical perspective of how the project began and go on to discuss its current feature set. ORCA has grown into a rather comprehensive general-purpose package for theoretical research in all areas of chemistry and many neighboring disciplines such as materials sciences and biochemistry. ORCA features density functional theory, a range of wavefunction based correlation methods, semi-empirical methods, and even force-field methods. A range of solvation and embedding models is featured as well as a complete intrinsic to ORCA quantum mechanics/molecular mechanics engine. A specialty of ORCA always has been a focus on transition metals and spectroscopy as well as a focus on applicability of the implemented methods to “real-life” chemical applications involving systems with a few hundred atoms. In addition to being efficient, user friendly, and, to the largest extent possible, platform independent, ORCA features a number of methods that are either unique to ORCA or have been first implemented in the course of the ORCA development. Next to a range of spectroscopic and magnetic properties, the linear- or low-order single- and multi-reference local correlation methods based on pair natural orbitals (domain based local pair natural orbital methods) should be mentioned here. Consequently, ORCA is a widely used program in various areas of chemistry and spectroscopy with a current user base of over 22 000 registered users in academic research and in industry.

The Journal of Chemical Physics, Volume 152, Issue 20, May 2020.
CRYSTAL is a periodic ab initio code that uses a Gaussian-type basis set to express crystalline orbitals (i.e., Bloch functions). The use of atom-centered basis functions allows treating 3D (crystals), 2D (slabs), 1D (polymers), and 0D (molecules) systems on the same grounds. In turn, all-electron calculations are inherently permitted along with pseudopotential strategies. A variety of density functionals are implemented, including global and range-separated hybrids of various natures and, as an extreme case, Hartree–Fock (HF). The cost for HF or hybrids is only about 3–5 times higher than when using the local density approximation or the generalized gradient approximation. Symmetry is fully exploited at all steps of the calculation. Many tools are available to modify the structure as given in input and simplify the construction of complicated objects, such as slabs, nanotubes, molecules, and clusters. Many tensorial properties can be evaluated by using a single input keyword: elastic, piezoelectric, photoelastic, dielectric, first and second hyperpolarizabilities, etc. The calculation of infrared and Raman spectra is available, and the intensities are computed analytically. Automated tools are available for the generation of the relevant configurations of solid solutions and/or disordered systems. Three versions of the code exist: serial, parallel, and massive-parallel. In the second one, the most relevant matrices are duplicated on each core, whereas in the third one, the Fock matrix is distributed for diagonalization. All the relevant vectors are dynamically allocated and deallocated after use, making the code very agile. CRYSTAL can be used efficiently on high performance computing machines up to thousands of cores.

The Journal of Chemical Physics, Volume 152, Issue 8, February 2020.
The multiconfiguration time-dependent Hartree (MCTDH) method is a powerful method for solving the time-dependent Schrödinger equation in quantum molecular dynamics. It is, however, hampered by the so-called curse of dimensionality which results in exponential scaling with respect to the number of degrees of freedom in the system and, thus, limits its applicability to small- and medium-sized molecules. To avoid this scaling, we derive equations of motion for a series of truncated MCTDH methods using a many-mode second-quantization formulation where the configuration space is restricted based on mode-combination levels as also done in the vibrational configuration interaction and vibrational coupled cluster methods for solving the time-independent Schrödinger equation. The full MCTDH wave function is invariant with respect to the choice of constraint (or gauge) operators, but restricting the configuration space removes this invariance. We, thus, analyze the remaining redundancies and derive equations for variationally optimizing the non-redundant matrix elements of the constraint operators. As an alternative, we also present a constraint that keeps the density matrices block diagonal during the propagation and the two choices are compared. Example calculations are performed on formyl fluoride and a series of high-dimensional Henon–Heiles potentials. The results show that the MCTDH[n] methods can be applied to large systems and that an optimal choice of constraint operators is key to obtaining the correct physical behavior of the wave function.

The Journal of Chemical Physics, Volume 152, Issue 4, January 2020.
Understanding native point defects is fundamental in order to comprehend the properties of TiO2 anatase in technological applications. The previous first-principles reports of defect-relevant quantities, such as formation energies and charge transition levels, are, however, scattered over a wide range. We perform a comparative study employing different approaches based on semilocal with Hubbard correction (DFT+U) and screened hybrid functionals in order to investigate the dependence defect properties on the employed computational method. While the defects in TiO2 anatase, as in most transition-metal oxides, generally induce the localization of electrons or holes on atomic sites, we notice that, provided an alignment of the valence bands has been performed, the calculated defect formation energies and transition levels using semilocal functionals are in a fair agreement with those obtained using hybrid functionals. A similar conclusion can be reached for the thermochemistry of the Ti–O system and the limit values of the elemental chemical potentials. We interpret this as a cancellation of error between the self-interaction error and the overbinding of the O2 molecule in semilocal functionals. Inclusion of a U term in the electron Hamiltonian offers a convenient way for obtaining more precise geometric and electronic configurations of the defective systems.

The Journal of Chemical Physics, Volume 151, Issue 18, November 2019.
In this work, we present general and robust transferable principles for the construction of quantum-mechanically treated clusters in a solid-state embedding (SSE) approach, beyond the still prevalent trial and error approach. Thereby, we probe the quality of different cluster shapes on the accuracy of chemisorption energies of small molecules and small polaron formation energies at the rutile TiO2 (110) surface as test cases. Our analyses show that at least the binding energies and electronic structures in the form of the density of states tend to be quite robust already for small, nonoptimal cluster shapes. In contrast to that, the description of polaron formation can be dramatically influenced by the employed cluster geometry possibly leading to an erroneous energetic ordering or even to a wrong prediction of the polaronic states themselves. Our findings show that this is mainly caused by an inaccurate description of the Hartree potential at boundary and surrounding atoms, which are insufficiently compensated by the embedding environment. This stresses the importance of the cluster size and shape for the accuracy of general-purpose SSE models that do not have to be refitted for each new chemical question. Based on these observations, we derive some general design criteria for solid state embedded clusters.