Perspective: Fifty years of density-functional theory in chemical physics

van der Waals forces in density functional theory: a review of the vdW-DF method

A density functional theory (DFT) that accounts for van der Waals (vdW) interactions in condensed matter, materials physics, chemistry, and biology is reviewed. The insights that led to the construction of the Rutgers-Chalmers van der Waals density functional (vdW-DF) are presented with the aim of giving a historical perspective, while also emphasizing more recent efforts which have sought to improve its accuracy. In addition to technical details, we discuss a range of recent applications that illustrate the necessity of including dispersion interactions in DFT. This review highlights the value of the vdW-DF method as a general-purpose method, not only for dispersion bound systems, but also in densely packed systems where these types of interactions are traditionally thought to be negligible.

The lowest triplet states of bridged cis-2,2'-bithiophenes - theory vs. experiment

Theoretical methods that were previously used to give a good quantitative description of the 3(1)Bu state of trans-2,2'-bithiophene are applied to characterize the lowest triplet states of three bridged cis-2,2'-bithiophenes: 3,3'-cyclopentadithiophene (CPDT), 3,3'-dithienylpyrrole (DTP), and 3,3'-dithienylthiophene (DTT). By obtaining highly accurate reproductions of the phosphorescence spectra of all three compounds, we rationalize the observed vibronic activity, further explore the performance of the applied theoretical methods, and address the quality of the reported experimental spectra. Over the course of this study we have, first, characterized the changes in the electronic structures between the ground state and the lowest triplet state and, second, expressed the related geometrical differences in terms of the Huang-Rhys factors. The Huang-Rhys factors have then been used to generate theoretical emission spectra with vibronic resolution. The applied procedure has yielded quantitative reproductions of the previously reported experimental phosphorescence spectra of DTT and DTP. The experimental spectrum of CPDT, on the other hand, turned out to be considerably narrower and intensity-deficient in its low energy region when compared with the theoretical results. Our experimental reinvestigation of the CPDT phosphorescence has given a refined spectrum that is significantly wider than the previously reported one, and is in nearly quantitative agreement with the theoretical prediction. This enabled us to attribute the observed discrepancy to an experimental artifact associated with the sensitivity characteristics of the commonly used photomultipliers.

Assessment of density-functionals for describing the X(-) + CH3ONO2 gas-phase reactions with X = F, OH, CH2CN

The energetics of the ECO2, SN2@C and SN2@N channels of X(-) + CH3ONO2 (X = F, OH, CH2CN) gas-phase reactions were computed using the CCSD(T)/CBS method. This benchmark extends a previous study with X = OH [M. A. F. de Souza et al., J. Am. Chem. Soc., 2012, 134, 19004] and was used to ascertain the accuracy and robustness of nineteen density-functionals for describing these potential energy profiles (PEP) as well as the kinetic product distributions obtained from RRKM calculations. Assessments were based on the mean unsigned error (MUE), the mean signed error (MSE), the #best : #worst (BW) criterion and the statistical confidence interval (CI) for the MSE. In general, double-hybrid (DH) functionals perform better than the range-separated ones, and both are better than the global-hybrid functionals. Based on the MUE and CI criteria the B2GPPLYP, B2PLYP, M08-SO, BMK, ωB97X-D, CAM-B3LYP, M06, M08-HX, ωB97X and B97-K functionals show the best performance in the description of these PEPs. Within this set, the B2GPPLYP functional is the most accurate and robust. The RRKM results indicate that the DHs are the best for describing the selectivities of these reactions. Compared to CCSD(T), the B2PLYP method has a relative error of only ca. 1% for the selectivity and the accuracy to provide the correct conclusion concerning the nonstatistical behavior of these reactions.

Preface: Special topic on advances in density functional theory

This Special Topic Issue on the Advances in Density Functional Theory, published as a celebration of the fifty years of density functional theory, contains a retrospective article, a perspective article, and a collection of original research articles that showcase recent theoretical advances in the field. It provides a timely discussion reflecting a cross section of our understanding, and the theoretical and computational developments, which have significant implications in broad areas of sciences and engineering.

Technical advances in molecular simulation since the 1980s

This review describes how the theory and practice of molecular simulation have evolved since the beginning of the 1980s when the author started his career in this field. The account is of necessity brief and subjective and highlights the changes that the author considers have had significant impact on his research and mode of working.

Density functional theory for field emission from carbon nano-structures

Electron field emission is understood as a quantum mechanical many-body problem in which an electronic quasi-particle of the emitter is converted into an electron in vacuum. Fundamental concepts of field emission, such as the field enhancement factor, work-function, edge barrier and emission current density, will be investigated, using carbon nanotubes and graphene as examples. A multi-scale algorithm basing on density functional theory is introduced. We will argue that such a first principle approach is necessary and appropriate for field emission of nano-structures, not only for a more accurate quantitative description, but, more importantly, for deeper insight into field emission.

Structural, bonding, and electronic properties of the hexagonal ferroelectric and paraelectric phases of LuMnO3 compound: a density functional theory study

We have investigated the structural, bonding, and electronic properties of both ferroelectric (FE) and paraelectric (PE) phases of the hexagonal LuMnO3 compound using calculations based on density functional theory. The structural properties have been determined by employing the generalized gradient approximation with Perdew-Burke-Ernzerhof and Wu-Cohen parameterization. The bonding and electronic properties have been treated by recently developed modified Becke-Johnson exchange potential, which succeeded to open a band gap for both PE and FE phases, in agreement with experimental predictions. The Bader's topological analysis of electronic density showed that the character of the Lu-O axial bonds changes when the crystal exhibits the PE → FE structural transition. This fact is in agreement with experimental findings. The covalent character of the Lu-O bond significantly increases due to orbital hybridization between the Lu 5dz(2) and O 2pz-states. This bonding mechanism causes the ferroelectricity in the hexagonal LuMnO3 compound.

Computational organic chemistry: bridging theory and experiment in establishing the mechanisms of chemical reactions

Understanding the mechanisms of chemical reactions, especially catalysis, has been an important and active area of computational organic chemistry, and close collaborations between experimentalists and theorists represent a growing trend. This Perspective provides examples of such productive collaborations. The understanding of various reaction mechanisms and the insight gained from these studies are emphasized. The applications of various experimental techniques in elucidation of reaction details as well as the development of various computational techniques to meet the demand of emerging synthetic methods, e.g., C-H activation, organocatalysis, and single electron transfer, are presented along with some conventional developments of mechanistic aspects. Examples of applications are selected to demonstrate the advantages and limitations of these techniques. Some challenges in the mechanistic studies and predictions of reactions are also analyzed.

Modified Slater exchange potential with correct uniform electron gas limit

Bulat and Levy recently deduced an expansion for the exact-exchange potential whose leading term is Slater’s averaged exchange-charge potential modified through the inclusion of orbital eigenvalues. When used as a stand-alone approximation to the exact-exchange potential, this leading term is much more accurate than Slater’s original. We give an alternative derivation of this term and show that, unlike the Slater potential, it correctly reduces to the Dirac exchange potential (i.e., the local density approximation) for a uniform electron gas, provided that the zero-energy reference of orbital eigenvalues is chosen as the Fermi level of the system. The orbital-energy-modified Slater potential should also recover the Dirac exchange potential for neutral atoms in the limit of infinite nuclear charge, but in practice converges to this limit very slowly on account of extreme sensitivity to the choice of zero-energy reference around the Fermi level.

Anisotropic displacement parameters from dispersion-corrected DFT methods and their experimental validation by temperature-dependent X-ray diffraction

How reliably can anisotropic displacement parameters be derived from theory? Experiments and computations on pentachloropyridine shed new light on this question.

In search of the appropriate theoretically justified mixing coefficient in parameter-free hybrid functionals for computing the NMR parameters

The parameter-free hybrid density functionals, with theoretically justified mixing coefficients, are recommended to predict the NMR parameters.

Divide-and-conquer quantum mechanical material simulations with exascale supercomputers

Recent developments in large-scale materials science simulations, especially under the divide-and-conquer method, are reviewed. The pros and cons of the divide-and-conquer method are discussed. It is argued that the divide-and-conquer method, such as the linear-scaling 3D fragment method, is an ideal approach to take advantage of the heterogeneous architectures of modern-day supercomputers despite their relatively large prefactors among linear-scaling methods. Some developments in graphics processing unit (GPU) electronic structure calculations are also reviewed. The accelerators like GPU could be an essential part for the future exascale supercomputing.

Multiple environment single system quantum mechanical/molecular mechanical (MESS-QM/MM) calculations. 1. Estimation of polarization energies

In combined quantum mechanical/molecular mechanical (QM/MM) free energy calculations, it is often advantageous to have a frozen geometry for the quantum mechanical (QM) region. For such multiple-environment single-system (MESS) cases, two schemes are proposed here for estimating the polarization energy: the first scheme, termed MESS-E, involves a Roothaan step extrapolation of the self-consistent field (SCF) energy; whereas the other scheme, termed MESS-H, employs a Newton–Raphson correction using an approximate inverse electronic Hessian of the QM region (which is constructed only once). Both schemes are extremely efficient, because the expensive Fock updates and SCF iterations in standard QM/MM calculations are completely avoided at each configuration. They produce reasonably accurate QM/MM polarization energies: MESS-E can predict the polarization energy within 0.25 kcal/mol in terms of the mean signed error for two of our test cases, solvated methanol and solvated β-alanine, using the M06-2X or ωB97X-D functionals; MESS-H can reproduce the polarization energy within 0.2 kcal/mol for these two cases and for the oxyluciferin–luciferase complex, if the approximate inverse electronic Hessians are constructed with sufficient accuracy.

Control of single-molecule junction conductance of porphyrins via a transition-metal center

Using scanning tunneling microscope break-junction experiments and a new first-principles approach to conductance calculations, we report and explain low-bias charge transport behavior of four types of metal-porphyrin-gold molecular junctions. A nonequilibrium Green's function approach based on self-energy corrected density functional theory and optimally tuned range-separated hybrid functionals is developed and used to understand experimental trends quantitatively. Importantly, due to the localized d states of the porphyrin molecules, hybrid functionals are essential for explaining measurements; standard semilocal functionals yield qualitatively incorrect results. Comparing directly with experiments, we show that the conductance can change by nearly a factor of 2 when different metal cations are used, counter to trends expected from gas-phase ionization energies which are relatively unchanged with the metal center. Our work explains the sensitivity of the porphyrin conductance with the metal center via a detailed and quantitative portrait of the interface electronic structure and provides a new framework for understanding transport quantitatively in complex junctions involving molecules with localized d states of relevance to light harvesting and energy conversion.

Spectral and electronic properties of nitrosylcobalamin

Nitrosylcobalamin (NOCbl) is readily formed when Co(II)balamin reacts with nitric oxide (NO) gas. NOCbl has been implicated in the inhibition of various B12-dependent enzymes, as well as in the modulation of blood pressure and of the immunological response. Previous studies revealed that among the known biologically relevant cobalamin species, NOCbl possesses the longest bond between the Co ion and the axially bound 5,6-dimethylbenzimidazole base, which was postulated to result from a strong trans influence exerted by the NO ligand. In this study, various spectroscopic (electronic absorption, circular dichroism, magnetic circular dichroism, and resonance Raman) and computational (density functional theory (DFT) and time-dependent DFT) techniques were used to generate experimentally validated electronic structure descriptions for the "base-on" and "base-off" forms of NOCbl. Further insights into the principal Co-ligand bonding interactions were obtained by carrying out natural bond orbital analyses. Collectively, our results indicate that the formally unoccupied Co 3dz(2) orbital engages in a highly covalent bonding interaction with the filled NO π* orbital and that the Co-NO bond is strengthened further by sizable π-backbonding interactions that are not present in any other Co(III)Cbl characterized to date. Because of the substantial NO(-) to Co(III) charge donation, NOCbl is best described as a hybrid of Co(III)-NO(-) and Co(II)-NO(•) resonance structures. In contrast, our analogous computational characterization of a related species, superoxocobalamin, reveals that in this case a Co(III)-O2(-) description is adequate due to the larger oxidizing power of O2 versus NO. The implications of our results with respect to the unusual structural features and thermochromism of NOCbl and the proposed inhibition mechanisms of B12-dependent enzymes by NOCbl are discussed.

QM/MM molecular dynamics studies of metal binding proteins

Mixed quantum-classical (quantum mechanical/molecular mechanical (QM/MM)) simulations have strongly contributed to providing insights into the understanding of several structural and mechanistic aspects of biological molecules. They played a particularly important role in metal binding proteins, where the electronic effects of transition metals have to be explicitly taken into account for the correct representation of the underlying biochemical process. In this review, after a brief description of the basic concepts of the QM/MM method, we provide an overview of its capabilities using selected examples taken from our work. Specifically, we will focus on heme peroxidases, metallo-β-lactamases, α-synuclein and ligase ribozymes to show how this approach is capable of describing the catalytic and/or structural role played by transition (Fe, Zn or Cu) and main group (Mg) metals. Applications will reveal how metal ions influence the formation and reduction of high redox intermediates in catalytic cycles and enhance drug metabolism, amyloidogenic aggregate formation and nucleic acid synthesis. In turn, it will become manifest that the protein frame directs and modulates the properties and reactivity of the metal ions.

A new exchange–correlation functional free of delocalization and static correlation errors

A combination of weighted density approximation and classical mapping leads to a new exchange–correlation energy free of delocalization and static correlation errors in Kohn–Sham density functional theory.