Standard Electronic Structure Methods Research Articles

On the Thermodynamic Equivalence of Grand Canonical, Infinite-Size, and Capacitor-Based Models in First-Principle Electrochemistry.

First principles-based computational and theoretical methods are constantly evolving trying to overcome the many obstacles towards a comprehensive understanding of electrochemical processes on an atomistic level. One of the major challenges has been the determination of reaction energetics under a constant potential. Here, a theoretical framework was proposed applying standard electronic structure methods and extrapolating to the infinite-cell size limit where reactions do not alter the potential. Today, electronically grand canonical modifications to electronic structure methods, holding the potential constant by varying the number of electrons in a finite simulation cell, become increasingly popular. In this perspective, we show that these two schemes are thermodynamically equivalent. Further, we link these methods to capacitive models of the interface, in the limit that the capacitance of the charging components (whether continuum or atomistic) are equal and invariant along the reaction pathway. We benchmark the three approaches with an example of alkali cation adsorption on Pt(111) showing that all three approaches converge in the cases of Li, Na and K. For Cs, however, strong deviation from the ideal conditions leads to a spread in the respective results. We discuss the latter by highlighting the cases of broken equivalence and assumptions among the approaches.

Ligand Field Theory and Angular Overlap Model Based Analysis of the Electronic Structure of Homovalent Iron-Sulfur Dimers.

The electronic structure of multinuclear transition metal complexes is a highly challenging problem for quantum chemical methods. The problems to be solved for a successful analysis include the following: (1) many unpaired electrons leading to “highly entangled” wave functions that cannot be calculated by standard electronic structure methods, (2) drastic differences between the one-particle and many-particle spectra and a high density of low-lying states, and (3) the interpretation of such highly complex wave functions in chemical terms. In this work, we continue our research on oligonuclear clusters by presenting an in-depth analysis of the electronic structure of a prototypical iron–sulfur (Fe2S2) dimer. Accurate wave functions are obtained from a variety of advanced wave function based methods. The wave function results are interpreted in terms of an effective Hamiltonian that in turn is parametrized in terms of the angular overlap model (AOM) that provides the chemical insights that we are striving for. A hierarchical analysis allows us to interpret the local electronic structure in terms of the thiolate, sulfide ligands, and metal–metal interaction strengths. The many-particle spectrum is analyzed in terms of configurations involving ligand and metal centers. Finally, we are able to derive simple yet effective interpretations of ligand interaction strengths, the metal–metal interaction strength, and the low-lying many-particle spectrum of the Fe2S2 dimer.

Benchmarking the Accuracy of Seniority-Zero Wave Function Methods for Noncovalent Interactions.

In this paper, we scrutinize the ability of seniority-zero wave function-based methods to model different types of noncovalent interactions, such as hydrogen bonds, dispersion, and mixed noncovalent interactions as well as prototypical model systems with various contributions of dynamic and static electron correlation effects. Specifically, we focus on the pair Coupled Cluster Doubles (pCCD) ansatz combined with two different flavors of dynamic energy corrections, (i) based on a perturbation theory correction and (ii) on a linearized coupled cluster ansatz on top of pCCD. We benchmark these approaches against the A24 data set [ Řezáč and Hobza J. Chem. Theory Comput. 2013 , 9 , 2151 - 2155 .] extrapolated to the basis set limit and some model noncovalent complexes that feature covalent bond breaking. By dissecting different types of interactions in the A24 data set within the Symmetry-Adapted Perturbation Theory (SAPT) framework, we demonstrate that pCCD can be classified as a dispersion-free method. Furthermore, we found that both flavors of post-pCCD approaches represent encouraging and computationally more efficient alternatives to standard electronic structure methods to model weakly bound systems, resulting in small statistical errors. Finally, a linearized coupled cluster correction on top of pCCD proved to be most reliable for the majority of investigated systems, featuring smaller nonparallelity errors compared to perturbation-theory-based approaches.

Rare-earth/transition-metal magnets at finite temperature: Self-interaction-corrected relativistic density functional theory in the disordered local moment picture

Atomic-scale computational modeling of technologically relevant permanent magnetic materials faces two key challenges. First, a material's magnetic properties depend sensitively on temperature, so the calculations must account for thermally induced magnetic disorder. Second, the most widely-used permanent magnets are based on rare-earth elements, whose highly localized 4$f$ electrons are poorly described by standard electronic structure methods. Here, we take two established theories, the disordered local moment picture of thermally induced magnetic disorder and self-interaction-corrected density functional theory, and devise a computational framework to overcome these challenges. Using the new approach, we calculate magnetic moments and Curie temperatures of the rare-earth cobalt (RECo$_5$) family for RE=Y--Lu. The calculations correctly reproduce the experimentally measured trends across the series and confirm that, apart from the hypothetical compound EuCo$_5$, SmCo$_5$ has the strongest magnetic properties at high temperature. An order-parameter analysis demonstrates that varying the RE has a surprisingly strong effect on the Co--Co magnetic interactions determining the Curie temperature, even when the lattice parameters are kept fixed. We propose the origin of this behavior is a small contribution to the density from $f$-character electrons located close to the Fermi level.

Metal-insulator transition in disordered systems from the one-body density matrix

The insulating state of matter can be probed by means of a ground state geometrical marker, which is closely related to the modern theory of polarization (based on a Berry phase). In the present work we show that this marker can be applied to determine the metal-insulator transition in disordered systems. In particular, for non-interacting systems the geometrical marker can be obtained from the configurational average of the norm-squared one-body density matrix, which can be calculated within open as well as periodic boundary conditions. This is in sharp contrast to a classification based on the static conductivity, which is only sensible within periodic boundary conditions. We exemplify the method by considering a simple lattice model, known to have a metal-insulator transition as a function of the disorder strength and demonstrate that the transition point can be obtained accurately from the one-body density matrix. The approach has a general {\it ab-initio} formulation and can be applied to realistic disordered materials by standard electronic structure methods.

Low-Lying ππ* States of Heteroaromatic Molecules: A Challenge for Excited State Methods.

The description of low-lying ππ* states of linear acenes by standard electronic structure methods is known to be challenging. Here, we broaden the framework of this problem by considering a set of fused heteroaromatic rings and demonstrate that standard electronic structure methods do not provide a balanced description of the two (typically) lowest singlet state (La and Lb) excitations. While the Lb state is highly sensitive to correlation effects, La suffers from the same drawbacks as charge transfer excitations. We show that the comparison between CIS/CIS(D) can serve as a diagnostic for detecting the two problematic excited states. Standard TD-DFT and even its spin-flip variant lead to inaccurate excitation energies and interstate gaps, with only a double hybrid functional performing somewhat better. The complication inherent to a balanced description of these states is so important that even CC2 and ADC(2) do not necessarily match the ADC(3) reference.

A perspective on nonresonant and resonant electronic response theory for time-dependent molecular properties

The development of electronic response theory in quantum chemistry has been reviewed, starting from the early 1970's and reaching the current state-of-the-art. The general theory has been applied to the calculation of a large number of spectroscopic parameters over the years, and it has been implemented for the majority of standard electronic structure methods. Two formulations of response theory, the Ehrenfest expectation value and the quasi-energy derivative formulation, have turned into leading alternatives for the derivation of computationally tractable expressions of response functions, and they are here reviewed with an attempt to, as far as possible, leave out technical details. A set of four steps are identified as common in derivations of response functions, and the two formulations are compared along this series of steps. Particular emphasis is given to the situation when the oscillation of the weak external electromagnetic field is in resonance with a transition frequency of the system. The formation of physically sound response functions in resonance regions of the spectrum is discussed in light of the causality condition and the Kramers-Kronig relations, and it is achieved in wave function theory by means of the introduction of relaxation parameters in a manner that mimics what one sees in density matrix theory. As a working example, equations are illustrated by their application to a two-state model for para-nitroaniline including the ground and the lowest charge-transfer state in the electric dipole approximation.

Ab initio methods for reactive potential surfaces

Case studies of ten reactions using a variety of standard electronic structure methods are presented. These case studies are used to illustrate the usefulness and shortcomings of these standard methods for various classes of reactions. Limited comparisons with experiment are made. The reactions studied include four radical-radical combinations, H + CH(3)--> CH(4), CH(3) + CH(3)--> C(2)H(6), H + HCO --> H(2)CO and CH(3) + HCO --> CH(3)CHO, three abstraction reactions, H + HO(2)--> H(2) + O(2), H + HCO --> H(2) + CO and CH(3) + HCO --> CH(4) + CO, a radical-molecule addition, H + HCCH --> C(2)H(3), and two molecular decompositions, H(2)CO --> H(2) + CO and CH(3)CHO --> CH(4) + CO. The electronic structure methods used are DFT, MP2, CCSD(T), QCISD(T), CASSCF, CASPT2, and CAS+1+2+QC.

Fast electronic structure methods for strongly correlated molecular systems

A short review is given of newly developed fast electronic structure methods that are designed to treat molecular systems with strong electron correlations, such as diradicaloid molecules, for which standard electronic structure methods such as density functional theory are inadequate. These new local correlation methods are based on coupled cluster theory within a perfect pairing active space, containing either a linear or quadratic number of pair correlation amplitudes, to yield the perfect pairing (PP) and imperfect pairing (IP) models. This reduces the scaling of the coupled cluster iterations to no worse than cubic, relative to the sixth power dependence of the usual (untruncated) coupled cluster doubles model. A second order perturbation correction, PP(2), to treat the neglected (weaker) correlations is formulated for the PP model. To ensure minimal prefactors, in addition to favorable size-scaling, highly efficient implementations of PP, IP and PP(2) have been completed, using auxiliary basis expansions. This yields speedups of almost an order of magnitude over the best alternatives using 4-center 2-electron integrals. A short discussion of the scope of accessible chemical applications is given.

Electronic-structure-based molecular-dynamics method for large biological systems: Application to the 10 basepair poly(dG)⋅poly(dC) DNA double helix

Combining several recently developed theoretical techniques, we have developed an electronic-structure-based method for performing molecular-dynamical simulations of large biological systems. The essence of the method can be summarized in three points: (i) There are two energy scales in the Hamiltonian and each is treated differently---the strong intramolecular interactions are treated within approximate density-functional theory, whereas the weak intermolecular interactions (e.g., hydrogen bonds) are described within a simple theory that accounts for Coulomb, exchange, and hopping interactions between the weakly interacting fragments. (ii) A localized basis of atomic states is used, yielding sparse Hamiltonian and overlap matrices. (iii) The total energies and forces from the sparse Hamiltonian and overlap matrices are solved using a linear scaling technique to avoid the ${\mathrm{N}}^{3}$ scaling problem of standard electronic structure methods. As an initial benchmark and test case of the method, we performed calculations of a deoxyribonucleic acid (DNA) double-helix poly(dG)\ensuremath{\cdot}poly(dC) segment containing ten basepairs, with a total of 644 atoms. By a dynamical simulation, we obtained the minimum-energy geometry and the electronic structure of this DNA dehydrated segment, as well as the full dynamical matrix corresponding to the relaxed structure. The vibrational data and energy band gap obtained compare qualitatively well with previous experimental data and other theoretical results.

New Hamiltonian model for long-range electronic superexchange in complex molecular structures

The electronic superexchange interactions, which enable long-range electron transfer in complex molecular structures, such as proteins, are beyond the capacity of standard electronic structure methods due to their size, inhomogeneity; aperiodicity, and sensitivity to the many weak interactions between the nominally insulating atoms of the intervening medium. The inhomogeneous aperiodic lattice theory, presented here, is a novel strategy implemented as a quantum molecular model, designed to enable the calculation of electronic transfer matrix elements in large macromolecular systems by redesigning the electronic structure problem into a two-tiered approach