Dynamic and Nondynamic Electron Correlation Energy Decomposition Based on the Node of the Hartree-Fock Slater Determinant.

Distinguishing between dynamic and nondynamic electron correlation energy is a fundamental concept in quantum chemistry. It can be challenging to make a clear distinction between the two types of correlation energy or to determine their actual contributions in specific cases using wave function theory. This is because both single-reference and multireference methods cover both types of correlation energy to some extent. Fixed-node diffusion quantum Monte Carlo (FNDMC) accurately covers dynamic correlations, but it is limited in overall accuracy by the node of the trial wave function. We introduce a methodology for partitioning an exact electron correlation energy into its dynamic and nondynamic components. This is accomplished by restricting a ground-state solution from sharing its node with a spin-restricted Hartree-Fock Slater determinant. The FNDMC method is used as a tool to conveniently project out a lowest-energy state obeying such a boundary condition. The proposed approach provides an unambiguous and useful procedure for separating electron correlation energy, as demonstrated on multiple systems, including the He atom, bond breaking of H2, the parametric H2-H2 system, the Be-Ne atomic series with low- and high-spin states for C, N, and O atoms, and small molecules such as BH, HF, and CO at both equilibrium and elongated configurations, respectively.

Accuracy of Noncovalent Interactions Involving d-Elements by the 1-Determinant Fixed-Node Diffusion Monte Carlo Method with Effective Core Potentials.

A critical assessment of effective core potential (ECP)-based single-determinant (SD) fixed-node diffusion quantum Monte Carlo (FNDMC) accuracy in prototypical noncovalent closed-shell systems involving d-elements is presented. Careful analysis of biases and elimination of possible bias sources leads to two findings of practical importance for SD FNDMC in these systems. First, in some systems (HCu:HCu, HCu:CuH), SD FNDMC reveals large biases of interaction energy differences (significantly exceeding the target 2% relative error) vs a reliable coupled-cluster CCSD(T)/CBS (complete basis set) reference. Second, the leading error of SD FNDMC with ECPs was attributed to a higher nuclear charge Z of d-group (pseudo) atoms, when compared to sp elements, in line with a previously reported finding that aggregate SD FNDMC bias tends to increase in systems with higher electronic densities. Therefore, SD FNDMC should only be used with caution in systems with a large Z.

Benchmarking fundamental gap of Sc2C(OH)2 MXene by many-body methods.

Sc2C(OH)2 is a prototypical non-magnetic member of MXenes, a promising transition-metal-based 2D material family, with a direct bandgap. We provide here a benchmark of its fundamental gap Δ obtained from many-body GW and fixed-node diffusion Monte Carlo methods. Both approaches independently arrive at a similar value of Δ âˆ¼ 1.3 eV, suggesting the validity of both methods. Such a bandgap makes Sc2C(OH)2 a 2D semiconductor suitable for optoelectronic applications. The absorbance spectra and the first exciton binding energy (0.63 eV), based on the Bethe-Salpeter equation, are presented as well. The reported results may serve to delineate experimental uncertainties and enable selection of reasonable approximations such as density functional theory functionals, for use in modeling of related MXenes.

Noncovalent Interactions by the Quantum Monte Carlo Method: Strong Influence of Isotropic Jastrow Cutoff Radii.

We present a paradigmatic example of a strong effect of Jastrow cutoff radii setup on the accuracy of noncovalent interaction energy differences within one-determinant Slater-Jastrow fixed-node diffusion Monte Carlo (1FNDMC) simulations using isotropic Jastrow terms and effective-core potentials. Analysis of total energies, absolute and relative errors, and local energy variance of energy differences vs the reference results suggests a simple procedure to marginalize the related biases. The presented data showcase improvements in dispersion-bounded systems within such a 1FNDMC method.

Fragmentation of natural orbital occupation numbers-based diagnostic of differential multireference character in complexes with hydrogen bonds.

We explore the possible route to approximate natural orbital occupation numbers-based diagnostic of differential multireference character of noncovalent energy differences by techniques based on many-body expansion. It turns out that two-body fragmentation of monomers may lead to a reasonable approximation of such a diagnostic in hydrogen-bonded complexes. The results are useful, for example, for assessment of the expected bias cancellation in energy differences of larger systems obtained by single-reference methods.

Fundamental gap of fluorographene by many-body GW and fixed-node diffusion Monte Carlo methods.

Fluorographene (FG) is a promising graphene-derived material with a large bandgap. Currently existing predictions of its fundamental gap (Δf) and optical gap (Δopt) significantly vary when compared with experiment. We provide here an ultimate benchmark of Δf for FG by many-body GW and fixed-node diffusion Monte Carlo (FNDMC) methods. Both approaches independently arrive at Δf ≈ 7.1 ± 0.1 eV. In addition, the Bethe-Salpeter equation enabled us to determine the first exciton binding energy, Eb = 1.92 eV. We also point to the possible misinterpretation problem of the results obtained for gaps of solids by FNDMC with single-reference trial wave functions of Bloch orbitals. We argue why instead of Δopt, in the thermodynamic limit, such an approach results in energy differences that rather correspond to Δf, and we also outline conditions when this case actually applies.

Fractional Charge by Fixed-Node Diffusion Monte Carlo Method.

Fixed-node diffusion Monte Carlo (FNDMC) method is a stochastic quantum many-body approach that has a great potential in electronic structure theory. We examine how FNDMC total energy E(N) satisfies exact constraints, linearity and derivative discontinuity, versus fractional electron number N, if combined with mean-field trial wave functions that miss such features. H and Cl atoms with fractional charge reveal that FNDMC method is well able to restore the piecewise linearity of E(N). The method uses ensemble and projector ingredients to achieve the correct charge localization. A water-solvated Cl^{-} complex illustrates superior performance of FNDMC method for charged noncovalent systems.

Toward Accurate Hydrogen Bonds by Scalable Quantum Monte Carlo.

Single-determinant (SD) fixed-node diffusion Monte Carlo (FNDMC) gains popularity as a benchmark method scalable to large noncovalent systems, although its accuracy limits are not yet fully mapped out. We report on an interesting example of significant SD FNDMC accuracy variations in middle-sized hydrogen-bonded dimer complexes, formic acid (FA) vs methanediol (MD), distinct by the maximum bond order (2 vs 1). While the traditional SD FNDMC schemes based on bias cancellation are capable of achieving benchmark (2%) accuracy for MD, this has not been the case for FA. We identify the leading systematic error source in energy differences and show that suitably designed Jastrow factors enable SD FNDMC to reach the reference accuracy for FA. This work clearly illustrates the varying accuracy of the present-day SD FNDMC at the 0.1 kcal/mol scale for a particular set of systems but also points out promising routes toward alleviation of these shortcomings, still within the single-reference framework.

Noncovalent Interactions by Fixed-Node Diffusion Monte Carlo: Convergence of Nodes and Energy Differences vs Gaussian Basis-Set Size.

Convergence of fixed-node (FN) shape and FN diffusion Monte Carlo (FNDMC) interaction energies is studied vs the Gaussian basis set saturation level in HF and CH4 dimers and one-determinant Slater-Jastrow trial wave functions (ΨT). The tested 25 distinct basis sets obtained by stepwise trimming of aug-VDZ and aug-VTZ bases suggest minimum basis set requirements to achieve reasonable results. A single selected trimmed basis set, about 2 times smaller in size than aug-VTZ, is extensively tested on a set of 12 noncovalent complexes including formic acid dimer, benzene-methane, or coronene-H2. The results indicate that equivalent noncovalent FNDMC energy differences are available at costs lower than assumed before. Additional insights from electron density differences and comparison of dimer vs monomer ΨT nodes explain this observation.

Bias cancellation in one-determinant fixed-node diffusion Monte Carlo: Insights from fermionic occupation numbers.

The accuracy of the fixed-node diffusion Monte Carlo (FNDMC) depends on the node location of the supplied trial state Ψ_{T}. The practical FNDMC approaches available for large systems rely on compact yet effective Ψ_{T}, most often containing an explicitly correlated single Slater determinant (SD). However, SD nodes may be better suited to one system than to another, which may possibly lead to inaccurate FNDMC energy differences. It remains a challenge how to estimate nonequivalence or appropriateness of SDs. Here we use the differences of a measure based on the Euclidean distance between the natural orbital occupation number (NOON) vector of the SD and the exact solution in the NOON vector space, which can be viewed as a measure of SD nonequivalence and as a qualitative measure of the expected degree of nondynamic-correlation-related bias in FNDMC energy differences. This is explored on a set of small noncovalent complexes and covalent bond breaking of Si_{2} vs N_{2}. It turns out that NOON-based measures well reflect the magnitude and sign of the bias present in the data available, thus providing insights into the nature of bias cancellation in SD FNDMC energy differences.

Room temperature organic magnets derived from sp3 functionalized graphene.

Materials based on metallic elements that have d orbitals and exhibit room temperature magnetism have been known for centuries and applied in a huge range of technologies. Development of room temperature carbon magnets containing exclusively sp orbitals is viewed as great challenge in chemistry, physics, spintronics and materials science. Here we describe a series of room temperature organic magnets prepared by a simple and controllable route based on the substitution of fluorine atoms in fluorographene with hydroxyl groups. Depending on the chemical composition (an F/OH ratio) and sp3 coverage, these new graphene derivatives show room temperature antiferromagnetic ordering, which has never been observed for any sp-based materials. Such 2D magnets undergo a transition to a ferromagnetic state at low temperatures, showing an extraordinarily high magnetic moment. The developed theoretical model addresses the origin of the room temperature magnetism in terms of sp2-conjugated diradical motifs embedded in an sp3 matrix and superexchange interactions via -OH functionalization.

A Nexus between Theory and Experiment: Non-Empirical Quantum Mechanical Computational Methodology Applied to Cucurbit[n]uril⋠Guest Binding Interactions.

A training set of eleven X-ray structures determined for biomimetic complexes between cucurbit[n]uril (CB[7 or 8]) hosts and adamantane-/diamantane ammonium/aminium guests were studied with DFT-D3 quantum mechanical computational methods to afford ΔGcalcd binding energies. A novel feature of this work is that the fidelity of the BLYP-D3/def2-TZVPP choice of DFT functional was proven by comparison with more accurate methods. For the first time, the CB[n]⋅guest complex binding energy subcomponents [for example, ΔEdispersion , ΔEelectrostatic , ΔGsolvation , binding entropy (-TΔS), and induced fit Edeformation(host) , Edeformation(guest) ] were calculated. Only a few weeks of computation time per complex were required by using this protocol. The deformation (stiffness) and solvation properties (with emphasis on cavity desolvation) of cucurbit[n]uril (n=5, 6, 7, 8) isolated host molecules were also explored by means of the DFT-D3 method. A high ρ2 =0.84 correlation coefficient between ΔGexptl and ΔGcalcd was achieved without any scaling of the calculated terms (at 298 K). This linear dependence was utilized for ΔGcalcd predictions of new complexes. The nature of binding, including the role of high energy water molecules, was also studied. The utility of introduction of tethered [-(CH2 )n NH3 ]+ amino loops attached to N,N-dimethyl-adamantane-1-amine and N,N,N',N'-tetramethyl diamantane-4,9-diamine skeletons (both from an experimental and a theoretical perspective) is presented here as a promising tool for the achievement of new ultra-high binding guests to CB[7] hosts. Predictions of not yet measured equilibrium constants are presented herein.

Noncovalent Interactions by Quantum Monte Carlo.

Quantum Monte Carlo (QMC) is a family of stochastic methods for solving quantum many-body problems such as the stationary Schrödinger equation. The review introduces basic notions of electronic structure QMC based on random walks in real space as well as its advances and adaptations to systems with noncovalent interactions. Specific issues such as fixed-node error cancellation, construction of trial wave functions, and efficiency considerations that allow for benchmark quality QMC energy differences are described in detail. Comprehensive overview of articles covers QMC applications to systems with noncovalent interactions over the last three decades. The current status of QMC with regard to efficiency, applicability, and usability by nonexperts together with further considerations about QMC developments, limitations, and unsolved challenges are discussed as well.

Reactivity of Fluorographene: A Facile Way toward Graphene Derivatives.

Fluorographene (FG) is a two-dimensional graphene derivative with promising application potential; however, its reactivity is not understood. We have systematically explored its reactivity in vacuum and polar environments. The C-F bond dissociation energies for homo- and heterolytic cleavage are above 100 kcal/mol, but the barrier of SN2 substitution is significantly lower. For example, the experimentally determined activation barrier of the FG reaction with NaOH in acetone equals 14 ± 5 kcal/mol. The considerable reactivity of FG indicates that it is a viable precursor for the synthesis of graphene derivatives and cannot be regarded as a chemical counterpart of Teflon.

Extensions and applications of the A24 data set of accurate interaction energies.

The A24 data set (Rezác and Hobza, J. Chem. Theory Comput. 2013, 9, 2151-2155) is a set of noncovalent complexes large enough to showcase various types of interactions yet small enough to make highly accurate calculations possible. It is intended for the testing of accurate computational methods which are then used as a benchmark in larger model systems. In this work, we improve the best estimate of the interaction energies in the set by updating their CCSD(T)/CBS and CCSDT(Q) components with calculations in larger basis sets. The data set is then used to test a large number of composite CCSD(T) approaches. Special attention is paid to the use of the explicitly correlated MP2-F12 method in these composite calculations. It is shown that an accuracy of 1-2% can be achieved with setups applicable to larger molecules. The effect of frozen natural orbital approximation on the accuracy of composite CCSD(T)/CBS calculations is also quantified. In four trivially saturated complexes where CCSDT(Q)/CBS data are now available, the convergence of the many-body correlation effects is assessed by fixed-node diffusion Monte Carlo (FN-DMC) calculations. A good agreement is achieved between FN-DMC and high-level coupled-cluster which represents an important cross-check of both approaches.

Chemical feasibility of the general acid/base mechanism of glmS ribozyme self-cleavage.

In numerous Gram-positive bacteria, the glmS ribozyme or catalytic riboswitch regulates the expression of glucosamine-6-phosphate (GlcN6P) synthase via site-specific cleavage of its sugar-phosphate backbone in response to GlcN6P ligand binding. Biochemical data have suggested a crucial catalytic role for an active site guanine (G40 in Thermoanaerobacter tengcongensis, G33 in Bacillus anthracis). We used hybrid quantum chemical/molecular mechanical (QM/MM) calculations to probe the mechanism where G40 is deprotonated and acts as a general base. The calculations suggest that the deprotonated guanine G40(-) is sufficiently reactive to overcome the thermodynamic penalty arising from its rare protonation state, and thus is able to activate the A-1(2'-OH) group toward nucleophilic attack on the adjacent backbone. Furthermore, deprotonation of A-1(2'-OH) and nucleophilic attack are predicted to occur as separate steps, where activation of A-1(2'-OH) precedes nucleophilic attack. Conversely, the transition state associated with the rate-determining step corresponds to concurrent nucleophilic attack and protonation of the G1(O5') leaving group by the ammonium moiety of the GlcN6P cofactor. Overall, our calculations help to explain the crucial roles of G40 (as a general base) and GlcN6P (as a general acid) during glmS ribozyme self-cleavage. In addition, we show that the QM/MM description of the glmS ribozyme self-cleavage reaction is significantly more sensitive to the size of the QM region and the quality of the QM-MM coupling than that of other small ribozymes.

Choosing a density functional for modeling adsorptive hydrogen storage: reference quantum mechanical calculations and a comparison of dispersion-corrected density functionals.

Hydrogen storage in carbonaceous materials and their derivatives is currently a widely investigated topic. The rational design of novel adsorptive materials is often attempted with the help of computational chemistry tools, in particular density functional theory (DFT). However, different exchange-correlation functionals provide a very wide range of hydrogen binding energies. The aim of this article is to offer high level QM reference data based on coupled-cluster singles and doubles calculations with perturbative triple excitations, CCSD(T), and a complete basis set limit estimate that can be used to assess the accuracy of various DFT-based predictions. For one complex, the CCSD(T) result is verified against diffusion quantum Monte Carlo calculations. Reference binding curves are calculated for two model compounds representing weak and strong hydrogen adsorption: coronene (-4.7 kJ mol(-1) per H2), and coronene modified with boron and lithium (-14.3 kJ mol(-1)). The reference data are compared to results obtained with widely used density functionals including pure DFT, M06, DFT-D3, PBE-TS, PBE + MBD, optB88-vdW, vdW-DF, vdW-DF2 and VV10. We find that whereas DFT-D3 shows excellent results for weak hydrogen adsorption on coronene, most of the less empirical density based dispersion functionals except VV10 overestimate this interaction. On the other hand, some of the less empirical density based dispersion functionals better describe stronger binding in the more polar coroB2Li22H2 complex which is one of realistic models for high-capacity hydrogen storage materials. Our results may serve as a guide for choosing suitable DFT methods for quickly evaluating hydrogen binding potential and as a reference for assessing the accuracy of the previously published DFT results.

The work functions of Au/Mg decorated Au(100), Mg(001), and AuMg alloy surfaces: a theoretical study.

A plane-wave density functional theory is used to predict the work functions of Au/Mg decorated Au(100), Mg(001), and stochiometric AuMg alloy surfaces. We find, that irrespective of the details, all Au/Mg systems containing Mg on the surface reveal the Mg-dominated work functions, i.e., significantly shifted toward the work function of clean Mg(001) surface. The reported analyses suggest, that this general trend stems from a strong charge transfer from Mg to Au and consequent enhancement of a surface dipole. The calculated properties of the AuMg alloy well agree to the experiment. The reported results may readily find applications in Au/Mg/AuMg surface physics and technology of metal/semiconductor contacts.

Quantum Monte Carlo for noncovalent interactions: an efficient protocol attaining benchmark accuracy.

Reliable theoretical prediction of noncovalent interaction energies, which are important e.g. in drug-design and hydrogen-storage applications, is one of the longstanding challenges of contemporary quantum chemistry. In this respect, the fixed-node diffusion Monte Carlo (FN-DMC) method is a promising alternative to the commonly used "gold standard" coupled-cluster CCSD(T)/CBS method due to its benchmark accuracy and favourable scaling, in contrast to other correlated wave function approaches. This work is focused on the analysis of protocols and possible trade-offs for FN-DMC estimations of noncovalent interaction energies, and proposes an efficient yet accurate computational protocol using simplified explicit correlation terms with a favorable O(N(3)) scaling. It achieves results in excellent agreement (mean unsigned error ∼0.2 kcal mol(-1)) with respect to the CCSD(T)/CBS data on a number of complexes, including benzene/hydrogen, the T-shape benzene dimer, stacked adenine-thymine complex and a set of small noncovalent complexes (A24). The high accuracy and reduced computational costs predestinate the reported protocol for practical interaction energy calculations of large noncovalent complexes, where the CCSD(T)/CBS is prohibitively expensive.