Atomic-scale representation and statistical learning of tensorial properties

This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian process regression, and in particular on the construction of structural representations, and the associated kernel functions, that are endowed with the geometric covariance properties compatible with those of the learning targets. We summarize the general formulation of such a symmetry-adapted Gaussian process regression model, and how it can be implemented based on a scheme that generalizes the popular smooth overlap of atomic positions representation. We give examples of the performance of this framework when learning the polarizability and the ground-state electron density of a molecule

Review of biorthogonal coupled cluster representations for electronic excitation

Single reference coupled-cluster (CC) methods for electronic excitation are based on a biorthogonal representation (bCC) of the (shifted) Hamiltonian in terms of excited CC states, also referred to as correlated excited (CE) states, and an associated set of states biorthogonal to the CE states, the latter being essentially configuration interaction (CI) configurations. The bCC representation generates a non-hermitian secular matrix, the eigenvalues representing excitation energies, while the corresponding spectral intensities are to be derived from both the left and right eigenvectors. Using the perspective of the bCC representation, a systematic and comprehensive analysis of the excited-state CC methods is given, extending and generalizing previous such studies. Here, the essential topics are the truncation error characteristics and the separability properties, the latter being crucial for designing size-consistent approximation schemes. Based on the general order relations for the bCC secular matrix and the (left and right) eigenvector matrices, formulas for the perturbation-theoretical (PT) order of the truncation errors (TEO) are derived for energies, transition moments, and property matrix elements of arbitrary excitation classes and truncation levels. In the analysis of the separability properties of the transition moments, the decisive role of the so-called dual ground state is revealed. Due to the use of CE states the bCC approach can be compared to so-called intermediate state representation (ISR) methods based exclusively on suitably orthonormalized CE states. As the present analysis shows, the bCC approach has decisive advantages over the conventional CI treatment, but also distinctly weaker TEO and separability properties in comparison with a full (and hermitian) ISR method

Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials

Quantum ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). Quantum ESPRESSO stands for "opEn Source Package for Research in Electronic Structure, Simulation, and Optimization". It is freely available to researchers around the world under the terms of the GNU General Public License. Quantum ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively-parallel architectures, and a great effort being devoted to user friendliness. Quantum ESPRESSO is evolving towards a distribution of independent and inter-operable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.Comment: 36 pages, 5 figures, resubmitted to J.Phys.: Condens. Matte

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy–cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe–Salpeter methods, second-order Møller–Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE’s functionality, including excited-state methods, RPA and Green’s function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE’s current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE’s development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy–cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe–Salpeter methods, second-order Møller–Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE’s functionality, including excited-state methods, RPA and Green’s function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE’s current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE’s development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted

Optoelectronic and Excitonic Properties of Oligoacenes: Substantial Improvements from Range-Separated Time-Dependent Density Functional Theory

The optoelectronic and excitonic properties in a series of linear acenes (naphthalene up to heptacene) are investigated using range-separated methods within time-dependent density functional theory (TDDFT). In these rather simple systems, it is well-known that TDDFT methods using conventional hybrid functionals surprisingly fail in describing the low-lying La and Lb valence states, resulting in large, growing errors for the La state and an incorrect energetic ordering as a function of molecular size. In this work, we demonstrate that the range-separated formalism largely eliminates both of these errors and also provides a consistent description of excitonic properties in these systems. We further demonstrate that re-optimizing the percentage of Hartree-Fock exchange in conventional hybrids to match wavefunction-based benchmark calculations still yields serious errors, and a full 100% Hartree-Fock range separation is essential for simultaneously describing both of the La and Lb transitions. Based on an analysis of electron-hole transition density matrices, we finally show that conventional hybrid functionals overdelocalize excitons and underestimate quasiparticle energy gaps in the acene systems. The results of our present study emphasize the importance of both a range-separated and asymptotically-correct contribution of exchange in TDDFT for investigating optoelectronic and excitonic properties, even for these simple valence excitations.Comment: Accepted by the Journal of Chemical Theory and Computatio

Recent advances in explicitly correlated coupled-cluster response theory for excited states and optical properties

The derivation of coupled-cluster response theory for explicitly correlated wavefunctions with terms linear in the interelectronic distance r12 (CC-R 12) or a function f12 thereof (CC-Fl 2) is reviewed and an implementation at the CCSD(R12) and CCSD(F12) for excitation energies and the linear, quadratic and cubic reponse functions is reported for ansätze 1 and 2. We discuss the results of first applications for vertical excitation energies, excited state equilibrium structures and vibrational frequencies, polarizabilities and first and second hyperpolarizabilities with focus on present limitations and future prospects of the approach. We show in particular that the standard choice of the geminal functions and wavefunction expansion can in certain cases lead to a bias towards the unperturbed ground state and how this can be avoided by extending the geminal space. If taken care of this, in particular CCSD(Fl2)/ansatz 2 shows for the potential energy curves of excited states and for optical properties a similar enhanced basis set convergence of the correlation contribution due to connected double excitations as for ground state energies. For diffuse excited states and hyperpolarizbilities the correlation contribution converges with CCSD(F12)/ansatz 2 often faster than orbital relaxation contributions. The convergence of the latter can be improved by allowing single excitations into a space spanned by a complementary auxiliary basis set.link_to_subscribed_fulltex