Quantitative estimation of localization errors of 3 d transition metal pseudopotentials in diffusion Monte Carlo

The necessarily approximate evaluation of non-local pseudopotentials in diffusion Monte Carlo (DMC) introduces localization errors. We estimate these errors for two families of non-local pseudopotentials for the first-row transition metal atoms Sc-Zn using an extrapolation scheme and multideterminant wavefunctions. Sensitivities of the error in the DMC energies to the Jastrow factor are used to estimate the quality of two sets of pseudopotentials with respect to locality error reduction. The locality approximation and T-moves scheme are also compared for accuracy of total energies. After estimating the removal of the locality and T-moves errors, we present the range of fixed-node energies between a single determinant description and a full valence multideterminant complete active space expansion. The results for these pseudopotentials agree with previous findings that the locality approximation is less sensitive to changes in the Jastrow than T-moves yielding more accurate total energies, however not necessarily more accurate energy differences. For both the locality approximation and T-moves, we find decreasing Jastrow sensitivity moving left to right across the series Sc-Zn. The recently generated pseudopotentials of Krogel et al. [Phys. Rev. B 93, 075143 (2016)] reduce the magnitude of the locality error compared with the pseudopotentials of Burkatzki et al. [J. Chem. Phys. 129, 164115 (2008)] by an average estimated 40% using the locality approximation. The estimated locality error is equivalent for both sets of pseudopotentials when T-moves is used. For the Sc-Zn atomic series with these pseudopotentials, and using up to three-body Jastrow factors, our results suggest that the fixed-node error is dominant over the locality error when a single determinant is used

Correction: CO2 induced phase transitions in diamine-appended metal-organic frameworks.

[This corrects the article DOI: 10.1039/C5SC01828E.]

Correction: CO2 induced phase transitions in diamine-appended metal-organic frameworks (Chemical Science (2015) 6 (5177-5185) DOI: 10.1039/c5sc01828e)

The authors regret that there are some discrepancies reproducing the data in the original article due to the determined coordinates not being the fully optimised geometries. The authors have provided more information as follows. In the manuscript entitled \u27CO2 induced phase transitions in diamine-appended metal-organic frameworks\u27, minor errors with the attached coordinates and energies reported in the paper have recently been identified. In this communication, we correct these errors. Here, we present updated optimized geometries and binding energies. We also take this opportunity to include an extended computational details section to ensure reproducibility. In addition, we show that the overall conclusions of the paper are not affected by these changes. A detailed comparison with the results reported by Lee et al.1 revealed that the DFT optimization of the coordinates provided with the manuscript do not lead to the values reported in the manuscript, and they warrant correction. Corrected coordinates and updated tables (Tables 1-7) and figures (Fig. 1, 2, 4 and 5) are included here for calculations using the PBE functional. These structures have been repeated using a slightly tighter force threshold than in the original manuscript (details below). The M06-L calculations reported in the original manuscript are not revisited since they were performed to assess the role of dispersion. Since the publication of our work in 2015, a far more detailed study of this effect has been published by one of the authors rendering these M06-L calculations unnecessary and we refer readers interested in the role of dispersion on the carbamate formation to this more recent study by Lee et al.1 In addition to correcting our DFT calculations, we examine the effects of the revised DFT values on the lattice model in this work.We recompute the lattice model with the M06-L and PBE values fromthe original manuscript as well as the corrected PBE values reported below (Fig. 6-8 and Tables 8-10). In all three sets of isotherm plots the ordering is preserved but the inflection points are spaced differently with the new PBE numbers, leading to quantitative differences that are nonetheless qualitatively similar to previous work. Finally, we discuss different ways that CO2 can coordinate to the metal binding site, as shown in Fig. 3. We should have notedmore clearly in ourmanuscript that these were starting configurations and not necessarily the final converged structures since our goal was to try several starting geometries to determine which coordination environment around the metal site was lowest in energy. Take for example bidentate insertion. Chemical intuition suggests that this structure could rotate to one that has only one CO2 oxygen center closer to the metal than the other and we observe this in our optimized structure. The resulting geometries we obtained for the starting arrangements noted in the figure are higher in energy than the chain model as reported in our original paper.We wish to emphasize that at the time of our 2015 study, our objective was to understand whether or not CO2 was bound to the metal and if one-dimensional chain formation could lead to a step in the adsorption isotherm. It has since become clear that a far more thorough study of the arrangements of the amines is required to truly understand competing amine arrangements preset in experiment. This was outside the scope of our work. Once more, these calculations are perhaps now outdated given work in the field in recent years. We again refer interested readers to a more recent study by Lee et al.1 1. Extended computational details to ensure reproducibility In the course of rectifying the error in our calculations, we wanted to ensure that all revised calculations were converged using the exact same protocol; therefore, we repeated the PBE calculations for the pair and chain models using updated computational details given here to ensure reproducibility. The M2(dobpdc) MOF contains six unsaturated metal sites per unit cell. To calculate the binding energies of CO2 in its amine appended analogue mmen-M2(dobpdc), one mmen ligand per CO2 was added per unit cell. The smaller sized ethylenediamine (en) was used to saturate the remaining amines not involved in CO2 binding. In the case of the pair mode, two mmen-amines are included per unit cell only. All DFT calculations were performed with periodic boundary conditions carried out using the VASP 5.4.4 package (original calculations were performed with VASP 5.3.3). The PBE functional was employed to examine the energetics of CO2 adsorption.3 On-site Hubbard U corrections were employed for metal d electrons.4 The U values are determined to reproduce oxidation energies in the respective metal oxides and are given in the tables below. The electron-ion interactions in these calculations were described with the projector augmented wave (PAW) method developed by Blöchl with an energy cutoff of 550 eV.5 This combination of the PBE functional, PAW scheme, and energy cutoff was used for full geometry optimization of the various species investigated until the forces on all atoms were smaller than 0.02 eV Å-1 and the SCF convergence was set to 1 × 10-7 eV. Given the large size of the unit cell and the tests with other numbers of K-points from the original study, only results obtained from G-point calculations are reported here. Finally, heats of adsorption are now reported below along with E + ZPE values, while in the original manuscript only E + ZPE were reported. No changes were made to how the vibrational corrections were computed; however, we have included some additional details to ensure reproducibility.6 Harmonic vibrational modes (ωi) were computed for CO2 in the gas phase and its bound product state (amine-CO2-MOF complex). The framework itself was taken to be rigid and only the vibrational modes associated with the motion of the amine, the metal center, first coordination sphere (oxygen atoms bound to the metal in the MOF backbone), and (if present) the bound CO2 were computed. Since the harmonic approximation breaks down for low frequency modes, we replaced all modes less than 50 cm-1 with 50 cm-1 when computing the zero-point and thermal energies. The following standard harmonic expressions were used to compute the vibrational corrections: Zero-point vibrational energy (ZPE) is: [Equation presented here] While for the bound product, the rotational and translational degrees of freedom of CO2 have been converted to additional vibrational modes allowing one to compute the thermal correction simply as: [Equation presented here] 2. Values for the chain model The chain model used in our original study included 1 mmen- and 5 en-amines. The values from the original paper are reported in Table 1. When we repeat these calculations using the procedure described in Section 1, we obtain the values in Table 2. In addition to the chain model described above (1 mmen- and 5 en-amines per unit cell), during our original study we performed calculations with another model that was not included in the manuscript since its values yielded results further from experiment. This model includes only 1 mmen-amine per unit cell (no other amines) and was used to test the assumption that the five enamines are indeed spectators with respect to the metal dependence of the binding energy. We present the results from this model in Table 3. In the original paper we noted that the energy and bond length trends are correlated and are consistent with the Irving-Williams series. This is no longer true for all metals under investigation, with Zn being an outlier. The results for Zn can be explained by more recent work.1 3. Values for the pair model The model used to compute the pair adsorption mechanisms included 2 mmen-amines and 0 en-amines. The values in the original paper are presented in Table 5. 4. Lattice model plots The lattice models to generate adsorption isotherms for these systems were run at one temperature (∼25 °C) using four different input parameters. First the M06-L and PBE values from the original paper were used once more as it has been some time since we have run the lattice model. Then the model is repeated with the new set of values from PBE. If we compare Fig. 7 and 8, the order is preserved, but the infliction points are spaced a bit differently. This is due to the scaling factor being constant and is something we scaled for each of the different systems as well. The slope is also a bit different, but not more then we should expect for this simple lattice model. Furthermore, we only ever aimed to reproduce the step and the order of the metals. Any finer details cannot be expected to be obtained from this model. The exact values used to compute the isotherms are given in the tables below. The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers

MnNiO3 revisited with modern theoretical and experimental methods

MnNiO3 is a strongly correlated transition metal oxide that has recently been investigated theoretically for its potential application as an oxygen-evolution photocatalyst. However, there is no experimental report on critical quantities such as the band gap or bulk modulus. Recent theoretical predictions with standard functionals such as LDA+U and HSE show large discrepancies in the band gaps (about 1.23 eV), depending on the nature of the functional used. Hence there is clearly a need for an accurate quantitative prediction of the band gap to gauge its utility as a photocatalyst. In this work, we present a diffusion quantum Monte Carlo study of the bulk properties of MnNiO3 and revisit the synthesis and experimental properties of the compound. We predict quasiparticle band gaps of 2.0(5) eV and 3.8(6) eV for the majority and minority spin channels, respectively, and an equilibrium volume of 92.8 Å3, which compares well to the experimental value of 94.4 Å3. A bulk modulus of 217 GPa is predicted for MnNiO3. We rationalize the difficulty for the formation of ordered ilmenite-type structure with specific sites for Ni and Mn to be potentially due to the formation of antisite defects that form during synthesis, which ultimately affects the physical properties of MnNiO3

CO2 induced phase transitions in diamine-appended metal-organic frameworks

Using a combination of density functional theory and lattice models, we study the effect of CO2 adsorption in an amine functionalized metal-organic framework. These materials exhibit a step in the adsorption isotherm indicative of a phase change. The pressure at which this step occurs is not only temperature dependent but is also metal center dependent. Likewise, the heats of adsorption vary depending on the metal center. Herein we demonstrate via quantum chemical calculations that the amines should not be considered firmly anchored to the framework and we explore the mechanism for CO2 adsorption. An ammonium carbamate species is formed via the insertion of CO2 into the M-Namine bonds. Furthermore, we translate the quantum chemical results into isotherms using a coarse grained Monte Carlo simulation technique and show that this adsorption mechanism can explain the characteristic step observed in the experimental isotherm while a previously proposed mechanism cannot. Furthermore, metal analogues have been explored and the CO2 binding energies show a strong metal dependence corresponding to the M-Namine bond strength. We show that this difference can be exploited to tune the pressure at which the step in the isotherm occurs. Additionally, the mmen-Ni-2(dobpdc) framework shows Langmuir like behavior, and our simulations show how this can be explained by competitive adsorption between the new model and a previously proposed model

The Mechanism of Carbon Dioxide Adsorption in an Alkylamine-Functionalized Metal-Organic Framework

The mechanism of CO2 adsorption in the amine-functionalized metal-organic framework mmen-Mg2(dobpdc) (dobpdc4- = 4,4′-dioxidobiphenyl-3,3′-dicarboxylate; mmen = N,N′- dimethylethylenediamine) was characterized by quantum-chemical calculations. The material was calculated to demonstrate 2:2 amine:CO2 stoichiometry with a higher capacity and weaker CO2 binding energy than for the 2:1 stoichiometry observed in most amine-functionalized adsorbents. We explain this behavior in the form of a hydrogen-bonded complex involving two carbamic acid moieties resulting from the adsorption of CO2 onto the secondary amines. © 2013 American Chemical Society

CrI3 revisited with a many-body ab initio theoretical approach

CrI3 has recently been shown to exhibit low-dimensional, long-range magnetic ordering from few layers to single layers of CrI3. The properties of CrI3 bulk and few-layered systems are uniquely defined by a combination of short-range intralayer and long-range interlayer interactions, including strong correlations, exchange, and spin-orbit coupling. Unfortunately, both the long-range van der Waals interactions, which are driven by dynamic, many-body electronic correlations, and the competing strong intralayer correlations, present a formidable challenge for the local or semilocal mean-field approximations employed in workhorse electronic structure approaches like density-functional theory. In this paper we employ a sophisticated many-body approach that can simultaneously describe long- and short-range correlations. We establish that the fixed-node diffusion Monte Carlo (FNDMC) method reproduces the experimental interlayer separation distance of bulk CrI3 for the high-temperature monoclinic phase with a reliable prediction of the interlayer binding energy. We subsequently employed the FNDMC results to benchmark the accuracy of several density-functional theory exchange-correlation approximations

Assessing Metal-Metal Multiple Bonds in Cr-Cr, Mo-Mo, and W-W Compounds and a Hypothetical U-U Compound: A Quantum Chemical Study Comparing DFT and Multireference Methods

To gain insights into the trends in metal–metal multiple bonding among the Group 6 elements, density functional theory has been employed in combination with multiconfigurational methods (CASSCF and CASPT2) to investigate a selection of bimetallic, multiply bonded compounds. For the compound [Ar-MM-Ar] (Ar=2,6-(C6H5)2-C6H3, M=Cr, Mo, W) the effect of the Ar ligand on the M2 core has been compared with the analogous [Ph-MM-Ph] (Ph=phenyl, M=Cr, Mo, W) compounds. A set of [M2(dpa)4] (dpa=2,2′-dipyridylamide, M=Cr, Mo, W, U) compounds has also been investigated. All of the compounds studied here show important multiconfigurational behavior. For the Mo2 and W2 compounds, the σ2π4δ2 configuration dominates the ground-state wavefunction, contributing at least 75 %. The Cr2 compounds show a more nuanced electronic structure, with many configurations contributing to the ground state. For the Cr, Mo, and W compounds the electronic absorption spectra have been studied, combining density functional theory and multireference methods to make absorption feature assignments. In all cases, the main features observed in the visible spectra may be assigned as charge-transfer bands. For all compounds investigated the Mayer bond order (MBO) and the effective bond order (EBO) were calculated by density functional theory and CASSCF methods, respectively. The MBO and EBO values share a similar trend toward higher values at shorter normalized metal–metal bond lengths