Density Functional Theory Exchange-correlation Functionals Research Articles

Excited state dynamics of Rhodamine B and its excitonically coupled dimer: A computational and experimental approach

Rhodamine B (RhB) is widely used for its high fluorescent quantum yield and strong absorption in the visible range of the spectrum; however, its facile aggregation in aqueous solutions dramatically affects its photophysical properties. Surprisingly, the excited state dynamics of rhodamines are not fully understood despite the extensive literature around them. Here, we present a complete picture of the photophysics of RhB and the most likely dimer formed in aqueous solution. We deconvolved the excited state dynamics of RhB and its non-covalent dimer using a combination of steady-state (SS) and time-resolved spectroscopic methods supported by density functional theory (DFT) and time-dependent DFT (TD-DFT). In particular, we have determined the dimerization equilibria constant in sodium perchlorate solutions and measured the dimer’s photo-induced charge separation and charge-recombination events. Additionally, we studied 12 DFT exchange–correlation functionals (XCF), and determined which are appropriate and which are not appropriate for studying and interpreting the excited state dynamics observed through femtosecond transient absorption (fsTA).

Efficient Mean-Field Simulation of Quantum Circuits Inspired by Density Functional Theory.

Exact simulations of quantum circuits (QCs) are currently limited to ∼50 qubits because the memory and computational cost required to store the QC wave function scale exponentially with qubit number. Therefore, developing efficient schemes for approximate QC simulations is a current research focus. Here, we show simulations of QCs with a method inspired by density functional theory (DFT), a widely used approach for studying many-electron systems. Our calculations can predict marginal single-qubit probabilities (SQPs) with over 90% accuracy in several classes of QCs with universal gate sets, using memory and computational resources linear in qubit number despite the formal exponential cost of the SQPs. This is achieved by developing a mean-field description of QCs and formulating optimal single- and two-qubit gate functionals─analogues of exchange-correlation functionals in DFT─to evolve the SQPs without computing the QC wave function. Current limitations and future extensions of this formalism are discussed.

First-principles molten salt phase diagrams through thermodynamic integration.

Precise prediction of phase diagrams in molecular dynamics simulations is challenging due to the simultaneous need for long time and large length scales and accurate interatomic potentials. We show that thermodynamic integration from low-cost force fields to neural network potentials trained using density-functional theory (DFT) enables rapid first-principles prediction of the solid-liquid phase boundary in the model salt NaCl. We use this technique to compare the accuracy of several DFT exchange-correlation functionals for predicting the NaCl phase boundary and find that the inclusion of dispersion interactions is critical to obtain good agreement with experiment. Importantly, our approach introduces a method to predict solid-liquid phase boundaries for any material at an abinitio level of accuracy, with the majority of the computational cost at the level of classical potentials.

Cheap Turns Superior: A Linear Regression-Based Correction Method to Reaction Energy from the DFT.

Workflows to predict chemical reaction networks based on density functional theory (DFT) are prone to systematic errors in reaction energy due to the extensive use of cheap DFT exchange-correlation functionals to limit computational cost. Recently, machine learning-based models are increasingly applied to mitigate this problem. However, machine learning models require systems similar to trained data, and the models often perform poorly for out-of-distribution systems. Here, we present a simple bond-based correction method that improves the accuracy of DFT-derived reaction energies. It is based on linear regression, and the correction terms for each bond are derived from reactions among the QM9 data set. We demonstrate the effectiveness of this method with three DFT functionals in three different rungs of Jacob's ladder. The simple correction method is effective for all rungs but especially so for the cheapest PBE functional. Finally, we applied the correction method to a few reactions with molecules significantly different from those in the QM9 data set that was used to fit the linear regression model. Once corrected by this method, we found that the DFT reaction energies for such out-of-distribution reactions are within 0.05 eV of the G4MP2 method.

A comparison of three DFT exchange-correlation functionals and two basis sets for the prediction of the conformation distribution of hydrated polyglycine.

The performance of three density functional theory (DFT) exchange-correlation functionals, namely, Perdew-Burke-Ernzerhof (PBE), BP86, and B3LYP, in predicting conformational distributions of a hydrated glycine peptide is tested with two different basis sets in the framework of adaptive force matching (AFM). The conformational distributions yielded the free energy profiles of the DFT functional and basis set combinations. Unlike traditional validations of potential energy and structural parameters, our approach allows the free energy of DFT to be validated. When compared to experimental distributions, the def2-TZVP basis set provides better agreement than a slightly trimmed aug-cc-pVDZ basis set. B3LYP is shown to be better than BP86 and PBE. The glycine model fitted against B3LYP-D3(BJ) with the def2-TZVP basis set is the most accurate and named the AFM2021 model for glycine. The AFM2021 glycine model provides better agreement with experimental J-coupling constants than C36m and ff14SB, although the margin is very small when compared to C36m. Our previously published alanine model is also refitted with the slightly simplified AFM2021 energy expression. This work shows good promise of AFM for developing force fields for a range of proteinogenic peptides using only DFT as reference.

An accurate machine learning calculator for the lithium-graphite system

Machine-learning potentials are accelerating the development of energy materials, especially in identifying phase diagrams and other thermodynamic properties. In this work, we present a neural network potential based on atom-centered symmetry function descriptors to model the energetics of lithium intercalation into graphite. The potential was trained on a dataset of over 9000 diverse lithium–graphite configurations that varied in applied stress and strain, lithium concentration, lithium–carbon and lithium–lithium bond distances, and stacking order to ensure wide sampling of the potential atomic configurations during intercalation. We calculated the energies of these structures using density functional theory (DFT) through the Bayesian error estimation functional with van der Waals correlation exchange-correlation functional, which can accurately describe the van der Waals interactions that are crucial to determining the thermodynamics of this phase space. Bayesian optimization, as implemented in Dragonfly, was used to select optimal set of symmetry function parameters, ultimately resulting in a potential with a prediction error of 8.24 meV atom−1 on unseen test data. The potential can predict energies, structural properties, and elastic constants at an accuracy comparable to other DFT exchange-correlation functionals at a fraction of the computational cost. The accuracy of the potential is also comparable to similar machine-learned potentials describing other systems. We calculate the open circuit voltage with the calculator and find good agreement with experiment, especially in the regime x ≥ 0.3, for x in Li x C6. This study further illustrates the power of machine learning potentials, which promises to revolutionize design and optimization of battery materials.

Density Functional Theory as a Data Science.

The development of density functional theory (DFT) functionals and physical corrections are reviewed focusing on the physical meanings and the semiempirical parameters from the viewpoint of data science. This review shows that DFT exchange-correlation functionals have been developed under many strict physical conditions with minimizing the number of the semiempirical parameters, except for some recent functionals. Major physical corrections for exchange-correlation function- als are also shown to have clear physical meanings independent of the functionals, though they inevitably require minimum semiempirical parameters dependent on the functionals combined. We, therefore, interpret that DFT functionals with physical corrections are the most sophisticated target functions that are physically legitimated, even from the viewpoint of data science.

Electronic structure benchmark calculations of inorganic and biochemical carboxylation reactions.

Carboxylation reactions represent a very special class of chemical reactions that is characterized by the presence of a carbon dioxide (CO2 ) molecule as reactive species within its global chemical equation. These reactions work as fundamental gear to accomplish the CO2 fixation and thus to build up more complex molecules through different technological and biochemical processes. In this context, a correct description of the CO2 electronic structure turns out to be crucial to study the chemical and electronic properties associated with this kind of reactions. Here, a systematic study of CO2 electronic structure and its contribution to different carboxylation reaction electronic energies has been carried out by means of several high-level ab initio post-Hartree Fock (post-HF) and density functional theory (DFT) calculations for a set of biochemistry and inorganic systems. We have found that for a correct description of the CO2 electronic correlation energy it is necessary to include post-CCSD(T) contributions (beyond the gold standard). These high-order excitations are required to properly describe the interactions of the four π-electrons associated with the two degenerated π-molecular orbitals of the CO2 molecule. Likewise, our results show that in some reactions it is possible to obtain accurate reaction electronic energy values with computationally less demanding methods when the error in the electronic correlation energy compensates between reactants and products. Furthermore, the provided post-HF reference values allowed to validating different DFT exchange-correlation functionals combined with different basis sets for chemical reactions that are relevant in biochemical CO2 fixing enzymes. © 2019 Wiley Periodicals, Inc.

Two-to-three dimensional transition in neutral gold clusters: The crucial role of van der Waals interactions and temperature

We predict the structures of neutral gas-phase gold clusters ($Au_n$, $n$ = 5$-$13) at finite temperatures based on free-energy calculations obtained by replica-exchange ab initio molecular dynamics. The structures of neutral $Au_5$$-$$Au_{13}$ clusters are assigned at 100 K based on a comparison of experimental far-infrared multiple photon dissociation spectra performed on Kr-tagged gold clusters with theoretical anharmonic IR spectra and free-energy calculations. The critical gold cluster size where the most stable isomer changes from planar to nonplanar is $Au_{11}$ (capped-trigonal prism, $D_{3h}$) at 100 K. However, at 300 K (i.e., room temperature), planar and nonplanar isomers may coexist even for $Au_8$, $Au_9$, and $Au_{10}$ clusters. Density-functional theory exchange-correlation functionals within the generalized gradient or hybrid approximation must be corrected for long-range van der Waals interactions to accurately predict relative gold cluster isomer stabilities. Our work gives insight into the stable structures of gas-phase gold clusters by highlighting the impact of temperature, and therefore the importance of free-energy over total energy studies, and long-range van der Waals interactions on gold cluster stability.

Performance of exchange-correlation functionals in density functional theory calculations for liquid metal: A benchmark test for sodium.

The performance of exchange-correlation functionals in density-functional theory (DFT) calculations for liquid metal has not been sufficiently examined. In the present study, benchmark tests of Perdew-Burke-Ernzerhof (PBE), Armiento-Mattsson 2005 (AM05), PBE re-parameterized for solids, and local density approximation (LDA) functionals are conducted for liquid sodium. The pair correlation function, equilibrium atomic volume, bulk modulus, and relative enthalpy are evaluated at 600 K and 1000 K. Compared with the available experimental data, the errors range from -11.2% to 0.0% for the atomic volume, from -5.2% to 22.0% for the bulk modulus, and from -3.5% to 2.5% for the relative enthalpy depending on the DFT functional. The generalized gradient approximation functionals are superior to the LDA functional, and the PBE and AM05 functionals exhibit the best performance. In addition, we assess whether the error tendency in liquid simulations is comparable to that in solid simulations, which would suggest that the atomic volume and relative enthalpy performances are comparable between solid and liquid states but that the bulk modulus performance is not. These benchmark test results indicate that the results of liquid simulations are significantly dependent on the exchange-correlation functional and that the DFT functional performance in solid simulations can be used to roughly estimate the performance in liquid simulations.

Toward Accurate Adsorption Energetics on Clay Surfaces.

Clay minerals are ubiquitous in nature, and the manner in which they interact with their surroundings has important industrial and environmental implications. Consequently, a molecular-level understanding of the adsorption of molecules on clay surfaces is crucial. In this regard computer simulations play an important role, yet the accuracy of widely used empirical force fields (FF) and density functional theory (DFT) exchange-correlation functionals is often unclear in adsorption systems dominated by weak interactions. Herein we present results from quantum Monte Carlo (QMC) for water and methanol adsorption on the prototypical clay kaolinite. To the best of our knowledge, this is the first time QMC has been used to investigate adsorption at a complex, natural surface such as a clay. As well as being valuable in their own right, the QMC benchmarks obtained provide reference data against which the performance of cheaper DFT methods can be tested. Indeed using various DFT exchange-correlation functionals yields a very broad range of adsorption energies, and it is unclear a priori which evaluation is better. QMC reveals that in the systems considered here it is essential to account for van der Waals (vdW) dispersion forces since this alters both the absolute and relative adsorption energies of water and methanol. We show, via FF simulations, that incorrect relative energies can lead to significant changes in the interfacial densities of water and methanol solutions at the kaolinite interface. Despite the clear improvements offered by the vdW-corrected and the vdW-inclusive functionals, absolute adsorption energies are often overestimated, suggesting that the treatment of vdW forces in DFT is not yet a solved problem.

Towards Efficient Orbital-Dependent Density Functionals for Weak and Strong Correlation.

We present a new paradigm for the design of exchange-correlation functionals in density-functional theory. Electron pairs are correlated explicitly by means of the recently developed second order Bethe-Goldstone equation (BGE2) approach. Here we propose a screened BGE2 (sBGE2) variant that efficiently regulates the coupling of a given electron pair. sBGE2 correctly dissociates H_{2} and H_{2}^{+}, a problem that has been regarded as a great challenge in density-functional theory for a long time. The sBGE2 functional is then taken as a building block for an orbital-dependent functional, termed ZRPS, which is a natural extension of the PBE0 hybrid functional. While worsening the good performance of sBGE2 in H_{2} and H_{2}^{+}, ZRPS yields a remarkable and consistent improvement over other density functionals across various chemical environments from weak to strong correlation.

Perspective: Treating electron over-delocalization with the DFT+U method.

Many people in the materials science and solid-state community are familiar with the acronym "DFT+U." For those less familiar, this technique uses ideas from model Hamiltonians that permit the description of both metals and insulators to address problems of electron over-delocalization in practical implementations of density functional theory (DFT). Exchange-correlation functionals in DFT are often described as belonging to a hierarchical "Jacob's ladder" of increasing accuracy in moving from local to non-local descriptions of exchange and correlation. DFT+U is not on this "ladder" but rather acts as an "elevator" because it systematically tunes relative energetics, typically on a localized subshell (e.g., d or f electrons), regardless of the underlying functional employed. However, this tuning is based on a metric of the local electron density of the subshells being addressed, thus necessitating physical or chemical or intuition about the system of interest. I will provide a brief overview of the history of how DFT+U came to be starting from the origin of the Hubbard and Anderson model Hamiltonians. This history lesson is necessary because it permits us to make the connections between the "Hubbard U" and fundamental outstanding challenges in electronic structure theory, and it helps to explain why this method is so widely applied to transition-metal oxides and organometallic complexes alike.

Water on BN doped benzene: a hard test for exchange-correlation functionals and the impact of exact exchange on weak binding.

Density functional theory (DFT) studies of weakly interacting complexes have recently focused on the importance of van der Waals dispersion forces, whereas the role of exchange has received far less attention. Here, by exploiting the subtle binding between water and a boron and nitrogen doped benzene derivative (1,2-azaborine) we show how exact exchange can alter the binding conformation within a complex. Benchmark values have been calculated for three orientations of the water monomer on 1,2-azaborine from explicitly correlated quantum chemical methods, and we have also used diffusion quantum Monte Carlo. For a host of popular DFT exchange-correlation functionals we show that the lack of exact exchange leads to the wrong lowest energy orientation of water on 1,2-azaborine. As such, we suggest that a high proportion of exact exchange and the associated improvement in the electronic structure could be needed for the accurate prediction of physisorption sites on doped surfaces and in complex organic molecules. Meanwhile to predict correct absolute interaction energies an accurate description of exchange needs to be augmented by dispersion inclusive functionals, and certain non-local van der Waals functionals (optB88- and optB86b-vdW) perform very well for absolute interaction energies. Through a comparison with water on benzene and borazine (B3N3H6) we show that these results could have implications for the interaction of water with doped graphene surfaces, and suggest a possible way of tuning the interaction energy.

Insight into the description of van der Waals forces for benzene adsorption on transition metal (111) surfaces

Exploring the role of van der Waals (vdW) forces on the adsorption of molecules on extended metal surfaces has become possible in recent years thanks to exciting developments in density functional theory (DFT). Among these newly developed vdW-inclusive methods, interatomic vdW approaches that account for the nonlocal screening within the bulk [V. G. Ruiz, W. Liu, E. Zojer, M. Scheffler, and A. Tkatchenko, Phys. Rev. Lett. 108, 146103 (2012)] and improved nonlocal functionals [J. Klimeš, D. R. Bowler, and A. Michaelides, J. Phys.: Condens. Matter 22, 022201 (2010)] have emerged as promising candidates to account efficiently and accurately for the lack of long-range vdW forces in most popular DFT exchange-correlation functionals. Here we have used these two approaches to compute benzene adsorption on a range of close-packed (111) surfaces upon which it either physisorbs (Cu, Ag, and Au) or chemisorbs (Rh, Pd, Ir, and Pt). We have thoroughly compared the performance between the two classes of vdW-inclusive methods and when available compared the results obtained with experimental data. By examining the computed adsorption energies, equilibrium distances, and binding curves we conclude that both methods allow for an accurate treatment of adsorption at equilibrium adsorbate-substrate distances. To this end, explicit inclusion of electrodynamic screening in the interatomic vdW scheme and optimized exchange functionals in the case of nonlocal vdW density functionals is mandatory. Nevertheless, some discrepancies are found between these two classes of methods at large adsorbate-substrate separations.

On the accuracy of van der Waals inclusive density-functional theory exchange-correlation functionals for ice at ambient and high pressures

Density-functional theory (DFT) has been widely used to study water and ice for at least 20 years. However, the reliability of different DFT exchange-correlation (xc) functionals for water remains a matter of considerable debate. This is particularly true in light of the recent development of DFT based methods that account for van der Waals (vdW) dispersion forces. Here, we report a detailed study with several xc functionals (semi-local, hybrid, and vdW inclusive approaches) on ice Ih and six proton ordered phases of ice. Consistent with our previous study [B. Santra, J. Klimeš, D. Alfè, A. Tkatchenko, B. Slater, A. Michaelides, R. Car, and M. Scheffler, Phys. Rev. Lett. 107, 185701 (2011)] which showed that vdW forces become increasingly important at high pressures, we find here that all vdW inclusive methods considered improve the relative energies and transition pressures of the high-pressure ice phases compared to those obtained with semi-local or hybrid xc functionals. However, we also find that significant discrepancies between experiment and the vdW inclusive approaches remain in the cohesive properties of the various phases, causing certain phases to be absent from the phase diagram. Therefore, room for improvement in the description of water at ambient and high pressures remains and we suggest that because of the stern test the high pressure ice phases pose they should be used in future benchmark studies of simulation methods for water.

The Curious Case of the Allyl Ligand: A Study in Applying the 18-Electron Rule

The 18-electron rule is an incredibly powerful tool for explaining the properties and reactivities of organometallic complexes. With the rule, however, comes the difficulty of choosing a method of implementing it, i.e. what many popular texts refer to as the “donor-pair” (ionic) method or the “neutral-ligand” method. The choice becomes particularly difficult when ligands can be counted in multiple ways via the donor-pair method, as in the case of the allyl ligand. In this investigation we hope to show that a choice of counting method can be chosen based on experimental intuition, as supported by a density functional theory (DFT) investigation. The natural electronic charge of metals, the η3-π-allyl (or simply the allyl) ligand, and the η3-cyclopropenyl ligand are discussed for a variety of organometallic complexes. A variety of DFT exchange-correlation functionals and basis sets, coupled with the Natural Population Analysis method of Landis and Weinhold, reveal the allyl ligand’s charge in a complex can be traced back to its experimental precursor. These results emphasize that the 18-electron rule is not merely a bookkeeping device and that the donor-pair method in the case of the allyl ligand holds more utility than the neutral-ligand method.

First-principles insight into the degeneracy of ground-state LiBH4structures

Recently, a number of ground-state structures of LiBH${}_{4}$ have been proposed, both from experimental and computational works. The results show controversy between computational and experimental ground-state crystal structures of LiBH${}_{4}$. In order to determine which is truly the lowest in energy, we study LiBH${}_{4}$ in a variety of crystal structures using density functional theory (DFT) calculations of the free energy ($T=0$ K total energy plus vibrational thermodynamics), employing a variety of DFT methods and exchange-correlation functionals. Our calculations show that the experimentally observed structures are lowest in energy in DFT. However, multiple LiBH${}_{4}$ structures are degenerate with the experimental ground-state crystal structure and there exists a relatively flat potential energy landscape between them. These degenerate structures include the recently theoretically predicted LiBH${}_{4}$ structure [Tekin, Caputo, and Z\"uettel, Phys. Rev. Lett. 104, 215501 (2010)], which the authors claimed to be 9.66 kJ/(mol LiBH${}_{4}$) (or $\ensuremath{\sim}$100 meV/fu) lower in energy than the experimentally XRD determined LiBH${}_{4}$ structure [Souli\'e, Renaudin, \ifmmode \check{C}\else \v{C}\fi{}ern\'y, and Yvon, J. Alloys Compd. 346, 200 (2002)]. Our calculations do not support these previous claims, and hence resolve this discrepancy between DFT and experiment.

Vibrational properties of alkyl monolayers on Si(111) surfaces: Predictions from ab-initio calculations

Vibrational properties of Si(111) surfaces terminated by different functional groups have been investigated using density functional theory (DFT). The variations in methyl-related frequencies in different chemical environments, e.g., in methane, methylsilane and ethylsilane, and the methyl- and ethyl-terminated Si(111) surfaces are well predicted by DFT within the local density approximation. In particular, DFT calculations provide useful information on trends and mode assignments in cases where the surface coverage and morphology are not well established experimentally, e.g., in the case of the ethyl-terminated Si(111) surface. Influences of DFT exchange-correlation functionals and anharmonic effects on computed vibrational frequencies are discussed.

Insufficient Hartree-Fock Exchange in Hybrid DFT Functionals Produces Bent Alkynyl Radical Structures.

Density functional theory (DFT) is often used to determine the electronic and geometric structures of molecules. While studying alkynyl radicals, we discovered that DFT exchange-correlation (XC) functionals containing less than ∼22% Hartree-Fock (HF) exchange led to qualitatively different structures than those predicted from ab initio HF and post-HF calculations or DFT XCs containing 25% or more HF exchange. We attribute this discrepancy to rehybridization at the radical center due to electron delocalization across the triple bonds of the alkynyl groups, which itself is an artifact of self-interaction and delocalization errors. Inclusion of sufficient exact exchange reduces these errors and suppresses this erroneous delocalization; we find that a threshold amount is needed for accurate structure determinations. Below this threshold, significant errors in predicted alkyne thermochemistry emerge as a consequence.