Selectivity of Electrochemical Ion Insertion into Manganese Dioxide Polymorphs.
ACS applied materials & interfaces
The ion insertion redox chemistry of manganese dioxide has diverse applications in energy storage, catalysis, and chemical separations. Unique properties derive from the assembly of Mn-O octahedra into polymorphic structures that can host protons and nonprotonic cations in interstitial sites. Despite many reports on individual ion-polymorph couples, much less is known about the selectivity of electrochemical ion insertion in MnO2. In this work, we use density functional theory to holistically compare the electrochemistry of AxMnO2 (where A = H+, Li+, Na+, K+, Mg2+, Ca2+, Zn2+, Al3+) in aqueous and nonaqueous electrolytes. We develop an efficient computational scheme demonstrating that Hubbard-U correction has a greater impact on calculating accurate redox energetics than choice of exchange-correlation functional. Using PBE+U, we find that for nonprotonic cations, ion selectivity depends on the oxygen coordination environments inside a polymorph. When H+ is present, however, the driving force to form hydroxyl bonds is usually stronger. In aqueous electrolytes, only three ion-polymorph pairs are thermodynamically stable within water's voltage stability window (Na+ and K+ in alpha-MnO2, and Li+ in lambda-MnO2), with all other ion insertion being metastable. We find Al3+ may insert into the delta, R, and lambda polymorphs across the full 2-electron redox of MnO2 at high voltage; however, electrolytes for multivalent ions must be designed to impede the formation of insoluble precipitates and facilitate cation desolvation. We also show that small ions coinsert with water in alpha-MnO2 to achieve greater coordination by oxygen, while solvation energies and kinetic effects dictate water coinsertion in delta-MnO2. Taken together, these findings explain reports of mixed ion insertion mechanisms in aqueous electrolytes and highlight promising design strategies for safe, high energy density electrochemical energy storage, desalination batteries, and electrocatalysts.
View details for DOI 10.1021/acsami.2c16589
View details for PubMedID 36546548
Investigation of the Structure of Atomically Dispersed NiNx Sites in Ni and N-Doped Carbon Electrocatalysts by 61Ni Mossbauer Spectroscopy and Simulations.
Journal of the American Chemical Society
Ni and nitrogen-doped carbons are selective catalysts for CO2 reduction to CO (CO2R), but the hypothesized NiNx active sites are challenging to probe with traditional characterization methods. Here, we synthesize 61Ni-enriched model catalysts, termed 61NiPACN, in order to apply 61Ni Mossbauer spectroscopy using synchrotron radiation (61Ni-SR-MS) to characterize the structure of these atomically dispersed NiNx sites. First, we demonstrate that the CO2R results and standard characterization techniques (SEM, PXRD, XPS, XANES, EXAFS) point to the existence of dispersed Ni active sites. Then, 61Ni-SR-MS reveal significant internal magnetic fields of 5.4 T, which is characteristic of paramagnetic, high-spin Ni2+, in the 61NiPACN samples. Finally, theoretical calculations for a variety of Ni-Nx moieties confirm that high-spin Ni2+ is stable in non-planar, tetrahedrally distorted geometries, which results in calculated isotropic hyperfine coupling that is consistent with 61Ni-SR-MS measurements.
View details for DOI 10.1021/jacs.2c09825
View details for PubMedID 36394993
- Efficient and Stable Acidic Water Oxidation Enabled by Low-Concentration, High-Valence Iridium Sites ACS ENERGY LETTERS 2022
- Unraveling Electronic Trends in O* and OH* Surface Adsorption in the MO2 Transition-Metal Oxide Series JOURNAL OF PHYSICAL CHEMISTRY C 2022; 126 (18): 7903-7909
- Cation-Dependent Multielectron Kinetics of Metal Oxide Splitting CHEMISTRY OF MATERIALS 2022; 34 (8): 3872-3881
- Overcoming Hurdles in Oxygen Evolution Catalyst Discovery via Codesign CHEMISTRY OF MATERIALS 2022; 34 (3): 899-910
- Water or Anion? Uncovering the Zn2+ Solvation Environment in Mixed Zn(TFSI)(2) and LiTFSI Water-in-Salt Electrolytes ACS ENERGY LETTERS 2021; 6 (10): 3458-3463
Origin of enhanced water oxidation activity in an iridium single atom anchored on NiFe oxyhydroxide catalyst.
Proceedings of the National Academy of Sciences of the United States of America
2021; 118 (36)
The efficiency of the synthesis of renewable fuels and feedstocks from electrical sources is limited, at present, by the sluggish water oxidation reaction. Single-atom catalysts (SACs) with a controllable coordination environment and exceptional atom utilization efficiency open new paradigms toward designing high-performance water oxidation catalysts. Here, using operando X-ray absorption spectroscopy measurements with calculations of spectra and electrochemical activity, we demonstrate that the origin of water oxidation activity of IrNiFe SACs is the presence of highly oxidized Ir single atom (Ir5.3+) in the NiFe oxyhydroxide under operating conditions. We show that the optimal water oxidation catalyst could be achieved by systematically increasing the oxidation state and modulating the coordination environment of the Ir active sites anchored atop the NiFe oxyhydroxide layers. Based on the proposed mechanism, we have successfully anchored Ir single-atom sites on NiFe oxyhydroxides (Ir0.1/Ni9Fe SAC) via a unique in situ cryogenic-photochemical reduction method that delivers an overpotential of 183 mV at 10 mA cm- 2 and retains its performance following 100 h of operation in 1 M KOH electrolyte, outperforming the reported catalysts and the commercial IrO2 catalysts. These findings open the avenue toward an atomic-level understanding of the oxygen evolution of catalytic centers under in operando conditions.
View details for DOI 10.1073/pnas.2101817118
View details for PubMedID 34465618
- Dynamics and Hysteresis of Hydrogen Intercalation and Deintercalation in Palladium Electrodes: A Multimodal In Situ X-ray Diffraction, Coulometry, and Computational Study CHEMISTRY OF MATERIALS 2021; 33 (15): 5872-5884
- Epitaxial Stabilization and Oxygen Evolution Reaction Activity of Metastable Columbite Iridium Oxide ACS APPLIED ENERGY MATERIALS 2021; 4 (4): 3074-3082
- Isolating the Electrocatalytic Activity of a Confined NiFe Motif within Zirconium Phosphate ADVANCED ENERGY MATERIALS 2021
Tuning electrochemially driven surface transformation in atomically flat LaNiO3 thin films for enhanced water electrolysis.
Structure-activity relationships built on descriptors of bulk and bulk-terminated surfaces are the basis for the rational design of electrocatalysts. However, electrochemically driven surface transformations complicate the identification of such descriptors. Here we demonstrate how the as-prepared surface composition of (001)-terminated LaNiO3 epitaxial thin films dictates the surface transformation and the electrocatalytic activity for the oxygen evolution reaction. Specifically, the Ni termination (in the as-prepared state) is considerably more active than the La termination, with overpotential differences of up to 150mV. A combined electrochemical, spectroscopic and density-functional theory investigation suggests that this activity trend originates from a thermodynamically stable, disordered NiO2 surface layer that forms during the operation of Ni-terminated surfaces, which is kinetically inaccessible when starting with a La termination. Our work thus demonstrates the tunability of surface transformation pathways by modifying a single atomic layer at the surface and that active surface phases only develop for select as-synthesized surface terminations.
View details for DOI 10.1038/s41563-020-00877-1
View details for PubMedID 33432142
- The role of atomic carbon in directing electrochemical CO(2) reduction to multicarbon products ENERGY & ENVIRONMENTAL SCIENCE 2021; 14 (1): 473–82
Guiding the Catalytic Properties of Copper for Electrochemical CO2 Reduction by Metal Atom Decoration.
ACS applied materials & interfaces
Tuning bimetallic effects is a promising strategy to guide catalytic properties. However, the nature of these effects can be difficult to assess and compare due to the convolution with other factors such as the catalyst surface structure and morphology and differences in testing environments. Here, we investigate the impact of atomic-scale bimetallic effects on the electrochemical CO2 reduction performance of Cu-based catalysts by leveraging a systematic approach that unifies protocols for materials synthesis and testing and enables accurate comparisons of intrinsic catalytic activity and selectivity. We used the same physical vapor deposition method to epitaxially grow Cu(100) films decorated with a small amount of noble or base metal atoms and a combination of experimental characterization and first-principles calculations to evaluate their physicochemical and catalytic properties. The results indicate that the metal atoms segregate to under-coordinated Cu sites during physical vapor deposition, suppressing CO reduction to oxygenates and hydrocarbons and promoting competing pathways to CO, formate, and hydrogen. Leveraging these insights, we rationalize bimetallic design principles to improve catalytic selectivity for CO2 reduction to CO, formate, oxygenates, or hydrocarbons. Our study provides one of the most extensive studies on Cu bimetallics for CO2 reduction, establishing a systematic approach that is broadly applicable to research in catalyst discovery.
View details for DOI 10.1021/acsami.1c09128
View details for PubMedID 34415714
- From electricity to fuels: Descriptors for C-1 selectivity in electrochemical CO2 reduction APPLIED CATALYSIS B-ENVIRONMENTAL 2020; 279
- Acidic Oxygen Evolution Reaction Activity-Stability Relationships in Ru-Based Pyrochlores ACS CATALYSIS 2020; 10 (20): 12182–96
- Active Learning Accelerated Discovery of Stable Iridium Oxide Polymorphs for the Oxygen Evolution Reaction CHEMISTRY OF MATERIALS 2020; 32 (13): 5854–63
- Interpreting Tafel behavior of consecutive electrochemical reactions through combined thermodynamic and steady state microkinetic approaches ENERGY & ENVIRONMENTAL SCIENCE 2020; 13 (2): 622–34
- Improved Oxygen Reduction Reaction Activity of Nanostructured CoS2 through Electrochemical Tuning ACS APPLIED ENERGY MATERIALS 2019; 2 (12): 8605–14
- Selective high-temperature CO2 electrolysis enabled by oxidized carbon intermediates NATURE ENERGY 2019; 4 (10): 846–55
- Machine Learning for Computational Heterogeneous Catalysis CHEMCATCHEM 2019; 11 (16): 3579–99
- Trends in Oxygen Electrocatalysis of 3 d-Layered (Oxy)(Hydro)Oxides CHEMCATCHEM 2019; 11 (15): 3423–31
Stabilization of reactive Co4O4 cubane oxygen-evolution catalysts within porous frameworks
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
2019; 116 (24): 11630–39
A major challenge to the implementation of artificial photosynthesis (AP), in which fuels are produced from abundant materials (water and carbon dioxide) in an electrochemical cell through the action of sunlight, is the discovery of active, inexpensive, safe, and stable catalysts for the oxygen evolution reaction (OER). Multimetallic molecular catalysts, inspired by the natural photosynthetic enzyme, can provide important guidance for catalyst design, but the necessary mechanistic understanding has been elusive. In particular, fundamental transformations for reactive intermediates are difficult to observe, and well-defined molecular models of such species are highly prone to decomposition by intermolecular aggregation. Here, we present a general strategy for stabilization of the molecular cobalt-oxo cubane core (Co4O4) by immobilizing it as part of metal-organic frameworks, thus preventing intermolecular pathways of catalyst decomposition. These materials retain the OER activity and mechanism of the molecular Co4O4 analog yet demonstrate unprecedented long-term stability at pH 14. The organic linkers of the framework allow for chemical fine-tuning of activity and stability and, perhaps most importantly, provide "matrix isolation" that allows for observation and stabilization of intermediates in the water-splitting pathway.
View details for DOI 10.1073/pnas.1815013116
View details for Web of Science ID 000471039700017
View details for PubMedID 31142656
View details for PubMedCentralID PMC6575163
Catalysis-Hub.org, an open electronic structure database for surface reactions.
2019; 6 (1): 75
We present a new open repository for chemical reactions on catalytic surfaces, available at https://www.catalysis-hub.org . The featured database for surface reactions contains more than 100,000 chemisorption and reaction energies obtained from electronic structure calculations, and is continuously being updated with new datasets. In addition to providing quantum-mechanical results for a broad range of reactions and surfaces from different publications, the database features a systematic, large-scale study of chemical adsorption and hydrogenation on bimetallic alloy surfaces. The database contains reaction specific information, such as the surface composition and reaction energy for each reaction, as well as the surface geometries andcalculational parameters, essential for data reproducibility. By providing direct access via the web-interface as well as a Python API, we seek to accelerate the discovery of catalytic materials for sustainable energy applications by enabling researchers to efficiently use the data as a basis for new calculations and model generation.
View details for DOI 10.1038/s41597-019-0081-y
View details for PubMedID 31138816
- The Role of Aluminum in Promoting Ni-Fe-OOH Electrocatalysts for the Oxygen Evolution Reaction ACS APPLIED ENERGY MATERIALS 2019; 2 (5): 3488–99
Catalysis-hub.org: An open electronic structure database for surface reactions and catalytic materials
AMER CHEMICAL SOC. 2019
View details for Web of Science ID 000478860501774
Systematic Investigation of Iridium-Based Bimetallic Thin Film Catalysts for the Oxygen Evolution Reaction in Acidic Media.
ACS applied materials & interfaces
Multimetallic Ir-based systems offer significant opportunities for enhanced oxygen evolution electrocatalysis by modifying the electronic and geometric properties of the active catalyst. Herein, a systematic investigation of bimetallic Ir-based thin films was performed to identify activity and stability trends across material systems for the oxygen evolution reaction (OER) in acidic media. Electron beam evaporation was used to co-deposit metallic films of Ir, IrSn2, IrCr, IrTi, and IrNi. The electrocatalytic activity of the electrochemically oxidized alloys was found to increase in the following order: IrTi < IrSn2 < Ir ∼ IrNi < IrCr. The IrCr system demonstrates two times the catalytic activity of Ir at 1.65 V versus RHE. Density functional theory calculations suggest that this enhancement is due to Cr active sites that have improved oxygen binding energetics compared to those of pure Ir oxide. This work identifies IrCr as a promising new catalyst system that facilitates reduced precious metal loadings for acid-based OER catalysis.
View details for DOI 10.1021/acsami.9b13697
View details for PubMedID 31442022
- Strongly Modified Scaling of CO Hydrogenation in Metal Supported TiO Nanostripes ACS CATALYSIS 2018; 8 (11): 10555–63
Understanding the apparent fractional charge of protons in the aqueous electrochemical double layer.
2018; 9 (1): 3202
A detailed atomic-scale description of the electrochemical interface is essential to the understanding of electrochemical energy transformations. In this work, we investigate the charge of solvated protons at the Pt(111) | H2O and Al(111) | H2O interfaces. Using semi-local density-functional theory as well as hybrid functionals and embedded correlated wavefunction methods as higher-level benchmarks, we show that the effective charge of a solvated proton in the electrochemical double layer or outer Helmholtz plane at all levels of theory is fractional, when the solvated proton and solvent band edges are aligned correctly with the Fermi level of the metal (EF). The observed fractional charge in the absence of frontier band misalignment arises from a significant overlap between the proton and the electron density from the metal surface, and results in an energetic difference between protons in bulk solution and those in the outer Helmholtz plane.
View details for PubMedID 30097564
- Understanding the apparent fractional charge of protons in the aqueous electrochemical double layer NATURE COMMUNICATIONS 2018; 9
Theoretical Investigations of the Electrochemical Reduction of CO on Single Metal Atoms Embedded in Graphene
ACS CENTRAL SCIENCE
2017; 3 (12): 1286–93
Single transition metal atoms embedded at single vacancies of graphene provide a unique paradigm for catalytic reactions. We present a density functional theory study of such systems for the electrochemical reduction of CO. Theoretical investigations of CO electrochemical reduction are particularly challenging in that electrochemical activation energies are a necessary descriptor of activity. We determined the electrochemical barriers for key proton-electron transfer steps using a state-of-the-art, fully explicit solvent model of the electrochemical interface. The accuracy of GGA-level functionals in describing these systems was also benchmarked against hybrid methods. We find the first proton transfer to form CHO from CO to be a critical step in C1 product formation. On these single atom sites, the corresponding barrier scales more favorably with the CO binding energy than for 211 and 111 transition metal surfaces, in the direction of improved activity. Intermediates and transition states for the hydrogen evolution reaction were found to be less stable than those on transition metals, suggesting a higher selectivity for CO reduction. We present a rate volcano for the production of methane from CO. We identify promising candidates with high activity, stability, and selectivity for the reduction of CO. This work highlights the potential of these systems as improved electrocatalysts over pure transition metals for CO reduction.
View details for PubMedID 29296669
View details for PubMedCentralID PMC5746853
- Formic Acid Dissociative Adsorption on NiO(111): Energetics and Structure of Adsorbed Formate JOURNAL OF PHYSICAL CHEMISTRY C 2017; 121 (50): 28001–6
Identifying the Active Surfaces of Electrochemically Tuned LiCoO2 for Oxygen Evolution Reaction
JOURNAL OF THE AMERICAN CHEMICAL SOCIETY
2017; 139 (17): 6270-6276
Identification of active sites for catalytic processes has both fundamental and technological implications for rational design of future catalysts. Herein, we study the active surfaces of layered lithium cobalt oxide (LCO) for the oxygen evolution reaction (OER) using the enhancement effect of electrochemical delithiation (De-LCO). Our theoretical results indicate that the most stable (0001) surface has a very large overpotential for OER independent of lithium content. In contrast, edge sites such as the nonpolar (112̅0) and polar (011̅2) surfaces are predicted to be highly active and dependent on (de)lithiation. The effect of lithium extraction from LCO on the surfaces and their OER activities can be understood by the increase of Co(4+) sites relative to Co(3+) and by the shift of active oxygen 2p states. Experimentally, it is demonstrated that LCO nanosheets, which dominantly expose the (0001) surface show negligible OER enhancement upon delithiation. However, a noticeable increase in OER activity (∼0.1 V in overpotential shift at 10 mA cm(-2)) is observed for the LCO nanoparticles, where the basal plane is greatly diminished to expose the edge sites, consistent with the theoretical simulations. Additionally, we find that the OER activity of De-LCO nanosheets can be improved if we adopt an acid etching method on LCO to create more active edge sites, which in turn provides a strong evidence for the theoretical indication.
View details for DOI 10.1021/jacs.7b02622
View details for Web of Science ID 000400802300043
- Water Dissociative Adsorption on NiO(111): Energetics and Structure of the Hydroxylated Surface ACS CATALYSIS 2016; 6 (11): 7377-7384
- Gold-supported cerium-doped NiOx catalysts for water oxidation NATURE ENERGY 2016; 1
Homogeneously dispersed multimetal oxygen-evolving catalysts.
2016; 352 (6283): 333-337
Earth-abundant first-row (3d) transition metal-based catalysts have been developed for the oxygen-evolution reaction (OER); however, they operate at overpotentials substantially above thermodynamic requirements. Density functional theory suggested that non-3d high-valency metals such as tungsten can modulate 3d metal oxides, providing near-optimal adsorption energies for OER intermediates. We developed a room-temperature synthesis to produce gelled oxyhydroxides materials with an atomically homogeneous metal distribution. These gelled FeCoW oxyhydroxides exhibit the lowest overpotential (191 millivolts) reported at 10 milliamperes per square centimeter in alkaline electrolyte. The catalyst shows no evidence of degradation after more than 500 hours of operation. X-ray absorption and computational studies reveal a synergistic interplay between tungsten, iron, and cobalt in producing a favorable local coordination environment and electronic structure that enhance the energetics for OER.
View details for DOI 10.1126/science.aaf1525
View details for PubMedID 27013427
- Enhancing Catalytic CO Oxidation over Co3O4 Nanowires by Substituting Co2+ with Cu2+ ACS CATALYSIS 2015; 5 (8): 4485-4491
Interface Controlled Oxidation States in Layered Cobalt Oxide Nanoislands on Gold
2015; 9 (3): 2445–53
Layered cobalt oxides have been shown to be highly active catalysts for the oxygen evolution reaction (OER; half of the catalytic "water splitting" reaction), particularly when promoted with gold. However, the surface chemistry of cobalt oxides and in particular the nature of the synergistic effect of gold contact are only understood on a rudimentary level, which at present prevents further exploration. We have synthesized a model system of flat, layered cobalt oxide nanoislands supported on a single crystal gold (111) substrate. By using a combination of atom-resolved scanning tunneling microscopy, X-ray photoelectron and absorption spectroscopies and density functional theory calculations, we provide a detailed analysis of the relationship between the atomic-scale structure of the nanoislands, Co oxidation states and substrate induced charge transfer effects in response to the synthesis oxygen pressure. We reveal that conversion from Co(2+) to Co(3+) can occur by a facile incorporation of oxygen at the interface between the nanoisland and gold, changing the islands from a Co-O bilayer to an O-Co-O trilayer. The O-Co-O trilayer islands have the structure of a single layer of β-CoOOH, proposed to be the active phase for the OER, making this system a valuable model in understanding of the active sites for OER. The Co oxides adopt related island morphologies without significant structural reorganization, and our results directly demonstrate that nanosized Co oxide islands have a much higher structural flexibility than could be predicted from bulk properties. Furthermore, it is clear that the gold/nanoparticle interface has a profound effect on the structure of the nanoislands, suggesting a possible promotion mechanism.
View details for DOI 10.1021/acsnano.5b00158
View details for Web of Science ID 000351791800021
View details for PubMedID 25693621
Identification of Highly Active Fe Sites in (Ni,Fe)OOH for Electrocatalytic Water Splitting
JOURNAL OF THE AMERICAN CHEMICAL SOCIETY
2015; 137 (3): 1305-1313
Highly active catalysts for the oxygen evolution reaction (OER) are required for the development of photoelectrochemical devices that generate hydrogen efficiently from water using solar energy. Here, we identify the origin of a 500-fold OER activity enhancement that can be achieved with mixed (Ni,Fe)oxyhydroxides (Ni(1-x)Fe(x)OOH) over their pure Ni and Fe parent compounds, resulting in one of the most active currently known OER catalysts in alkaline electrolyte. Operando X-ray absorption spectroscopy (XAS) using high energy resolution fluorescence detection (HERFD) reveals that Fe(3+) in Ni(1-x)Fe(x)OOH occupies octahedral sites with unusually short Fe-O bond distances, induced by edge-sharing with surrounding [NiO6] octahedra. Using computational methods, we establish that this structural motif results in near optimal adsorption energies of OER intermediates and low overpotentials at Fe sites. By contrast, Ni sites in Ni(1-x)Fe(x)OOH are not active sites for the oxidation of water.
View details for DOI 10.1021/ja511559d
View details for Web of Science ID 000348690100042
View details for PubMedID 25562406
Theoretical investigation of the activity of cobalt oxides for the electrochemical oxidation of water.
Journal of the American Chemical Society
2013; 135 (36): 13521-13530
The presence of layered cobalt oxides has been identified experimentally in Co-based anodes under oxygen-evolving conditions. In this work, we report the results of theoretical investigations of the relative stability of layered and spinel bulk phases of Co oxides, as well as the stability of selected surfaces as a function of applied potential and pH. We then study the oxygen evolution reaction (OER) on these surfaces and obtain activity trends at experimentally relevant electro-chemical conditions. Our calculated volume Pourbaix diagram shows that β-CoOOH is the active phase where the OER occurs in alkaline media. We calculate relative surface stabilities and adsorbate coverages of the most stable low-index surfaces of β-CoOOH: (0001), (0112), and (1014). We find that at low applied potentials, the (1014) surface is the most stable, while the (0112) surface is the more stable at higher potentials. Next, we compare the theoretical overpotentials for all three surfaces and find that the (1014) surface is the most active one as characterized by an overpotential of η = 0.48 V. The high activity of the (1014) surface can be attributed to the observation that the resting state of Co in the active site is Co(3+) during the OER, whereas Co is in the Co(4+) state in the less active surfaces. Lastly, we demonstrate that the overpotential of the (1014) surface can be lowered further by surface substitution of Co by Ni. This finding could explain the experimentally observed enhancement in the OER activity of Ni(y)Co(1-y)O(x) thin films with increasing Ni content. All energetics in this work were obtained from density functional theory using the Hubbard-U correction.
View details for DOI 10.1021/ja405997s
View details for PubMedID 23944254
Theoretical investigation of oxygen evolution reaction in layered cobalt oxides
AMER CHEMICAL SOC. 2013
View details for Web of Science ID 000323851304877
- Importance of Correlation in Determining Electrocatalytic Oxygen Evolution Activity on Cobalt Oxides JOURNAL OF PHYSICAL CHEMISTRY C 2012; 116 (39): 21077-21082
Pfaffian pairing wave functions in electronic-structure quantum Monte Carlo simulations
PHYSICAL REVIEW LETTERS
2006; 96 (13): 130201
We investigate the accuracy of trial wave functions for quantum Monte Carlo based on Pfaffian functional form with singlet and triplet pairing. Using a set of first row atoms and molecules we find that these wave functions provide very consistent and systematic behavior in recovering the correlation energies on the level of 95%. In order to get beyond this limit we explore the possibilities of multi-Pfaffian pairing wave functions. We show that a small number of Pfaffians recovers another large fraction of the missing correlation energy comparable to the larger-scale configuration interaction wave functions. We also find that Pfaffians lead to substantial improvements in fermion nodes when compared to Hartree-Fock wave functions.
View details for DOI 10.1103/PhysRevLett.96.130201
View details for Web of Science ID 000236612400001
View details for PubMedID 16711968