Expanding the Design Space of Constraints in Auxiliary-Field Quantum Monte Carlo.

We formulate and characterize a new constraint for auxiliary-field quantum Monte Carlo (AFQMC) applicable for general fermionic systems, which allows for the accumulation of phase in the random walk but disallows walkers with a magnitude of phase greater than π with respect to the trial wave function. For short imaginary times, before walkers accumulate sizable phase values, this approach is equivalent to exact free projection, allowing one to observe the accumulation of bias associated with the constraint and thus estimate its magnitude a priori. We demonstrate the stability of this constraint over arbitrary imaginary times and system sizes, highlighting the removal of noise due to the fermionic sign problem. Benchmark total energies for a variety of weakly and strongly correlated molecular systems reveal a distinct bias with respect to standard phaseless AFQMC, with a comparative increase in accuracy given sufficient quality of the trial wave function for the set of studied cases. We then take this constraint, termed linecut AFQMC (lc-AFQMC), and systematically release it (lcR-AFQMC), providing a route to obtain a smooth bridge between constrained AFQMC and the exact free projection results.

Accurate Quantum Chemical Reaction Energies for Lithium-Mediated Electrolyte Decomposition and Evaluation of Density Functional Approximations.

An important concern related to the performance of Li-ion batteries is the formation of a solid electrolyte interphase on the surface of the anode. This film is formed from the decomposition of electrolytes and can have important effects on the stability and performance. Here, we evaluate the decomposition pathway of ethylene carbonate and related organic electrolyte molecules using a series of density functional approximations and correlated wave function (WF) methods, including the coupled-cluster theory with single, double, and perturbative triple excitations [CCSD(T)] and auxiliary-field quantum Monte Carlo (AFQMC). We find that the transition state barrier associated with ring opening varies widely across different functionals, ranging from 3.01 to 17.15 kcal/mol, which can be compared to the value of 12.84 kcal/mol predicted by CCSD(T). This large variation underscores the importance of benchmarking against accurate WF methods. A performance comparison of all of the density functionals used in this study reveals that the M06-2X-D3 (a meta-hybrid GGA), CAM-B3LYP-D3 (a range-separated hybrid), and B2GP-PLYP-D3 (a double hybrid) perform the best, with average errors of about 1.50-1.60 kcal/mol compared to CCSD(T). We also compared the performance of the WF methods that are more scalable than CCSD(T), finding that DLPNO-CCSD(T) and phaseless AFQMC with a DFT trial wave function exhibit average errors of 1.38 and 1.74 kcal/mol, respectively.

Toward Benchmark-Quality Ab Initio Predictions for 3d Transition Metal Electrocatalysts: A Comparison of CCSD(T) and ph-AFQMC.

Generating accurate ab initio ionization energies for transition metal complexes is an important step toward the accurate computational description of their electrocatalytic reactions. Benchmark-quality data is required for testing existing theoretical methods and developing new ones but is complicated to obtain for many transition metal compounds due to the potential presence of both strong dynamical and static electron correlation. In this regime, it is questionable whether the so-called gold standard, coupled cluster with singles, doubles, and perturbative triples (CCSD(T)), provides the desired level of accuracy─roughly 1-3 kcal/mol. In this work, we compiled a test set of 28 3d metal-containing molecules relevant to homogeneous electrocatalysis (termed 3dTMV) and computed their vertical ionization energies (ionization potentials) with CCSD(T) and phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) in the def2-SVP basis set. A substantial effort has been made to converge away the phaseless bias in the ph-AFQMC reference values. We assess a wide variety of multireference diagnostics and find that spin-symmetry breaking of the CCSD wave function and the PBE0 density functional correlate well with our analysis of multiconfigurational wave functions. We propose quantitative criteria based on symmetry breaking to delineate correlation regimes inside of which appropriately performed CCSD(T) can produce mean absolute deviations from the ph-AFQMC reference values of roughly 2 kcal/mol or less and outside of which CCSD(T) is expected to fail. We also present a preliminary assessment of density functional theory (DFT) functionals on the 3dTMV set.

On the potentially transformative role of auxiliary-field quantum Monte Carlo in quantum chemistry: A highly accurate method for transition metals and beyond.

Approximate solutions to the ab initio electronic structure problem have been a focus of theoretical and computational chemistry research for much of the past century, with the goal of predicting relevant energy differences to within "chemical accuracy" (1 kcal/mol). For small organic molecules, or in general, for weakly correlated main group chemistry, a hierarchy of single-reference wave function methods has been rigorously established, spanning perturbation theory and the coupled cluster (CC) formalism. For these systems, CC with singles, doubles, and perturbative triples is known to achieve chemical accuracy, albeit at O(N7) computational cost. In addition, a hierarchy of density functional approximations of increasing formal sophistication, known as Jacob's ladder, has been shown to systematically reduce average errors over large datasets representing weakly correlated chemistry. However, the accuracy of such computational models is less clear in the increasingly important frontiers of chemical space including transition metals and f-block compounds, in which strong correlation can play an important role in reactivity. A stochastic method, phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC), has been shown to be capable of producing chemically accurate predictions even for challenging molecular systems beyond the main group, with relatively low O(N3 - N4) cost and near-perfect parallel efficiency. Herein, we present our perspectives on the past, present, and future of the ph-AFQMC method. We focus on its potential in transition metal quantum chemistry to be a highly accurate, systematically improvable method that can reliably probe strongly correlated systems in biology and chemical catalysis and provide reference thermochemical values (for future development of density functionals or interatomic potentials) when experiments are either noisy or absent. Finally, we discuss the present limitations of the method and where we expect near-term development to be most fruitful.

Targeted activation in localized protein environments via deep red photoredox catalysis.

State-of-the-art photoactivation strategies in chemical biology provide spatiotemporal control and visualization of biological processes. However, using high-energy light (λ < 500 nm) for substrate or photocatalyst sensitization can lead to background activation of photoactive small-molecule probes and reduce its efficacy in complex biological environments. Here we describe the development of targeted aryl azide activation via deep red-light (λ = 660 nm) photoredox catalysis and its use in photocatalysed proximity labelling. We demonstrate that aryl azides are converted to triplet nitrenes via a redox-centric mechanism and show that its spatially localized formation requires both red light and a photocatalyst-targeting modality. This technology was applied in different colon cancer cell systems for targeted protein environment labelling of epithelial cell adhesion molecule (EpCAM). We identified a small subset of proteins with previously known and unknown association to EpCAM, including CDH3, a clinically relevant protein that shares high tumour-selective expression with EpCAM.

A Localized-Orbital Energy Evaluation for Auxiliary-Field Quantum Monte Carlo.

Phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) has recently emerged as a promising method for the production of benchmark-level simulations of medium- to large-sized molecules because of its accuracy and favorable polynomial scaling with system size. Unfortunately, the memory footprints of standard energy evaluation algorithms are nontrivial, which can significantly impact timings on graphical processing units (GPUs) where memory is limited. Previous attempts to reduce scaling by taking advantage of the low-rank structure of the Coulombic integrals have been successful but exhibit high prefactors, making their utility limited to very large systems. Here we present a complementary cubic-scaling route to reduce memory and computational scaling based on the low rank of the Coulombic interactions between localized orbitals, focusing on the application to ph-AFQMC. We show that the error due to this approximation, which we term localized-orbital AFQMC (LO-AFQMC), is systematic and controllable via a single variable and that the method is computationally favorable even for small systems. We present results demonstrating robust retention of accuracy versus both experiment and full ph-AFQMC for a variety of test cases chosen for their potential difficulty for localized-orbital-based methods, including the singlet-triplet gaps of the polyacenes benzene through pentacene, the heats of formation for a set of Platonic hydrocarbon cages, and the total energy of ferrocene, Fe(Cp)2. Finally, we reproduce our previous result for the gas-phase ionization energy of Ni(Cp)2, agreeing with full ph-AFQMC to within statistical error while using less than 1/15th of the computer time.

Calculation of Metallocene Ionization Potentials via Auxiliary Field Quantum Monte Carlo: Toward Benchmark Quantum Chemistry for Transition Metals.

The accurate ab initio prediction of ionization energies is essential to understanding the electrochemistry of transition metal complexes in both materials science and biological applications. However, such predictions have been complicated by the scarcity of gas phase experimental data, the relatively large size of the relevant molecules, and the presence of strong electron correlation effects. In this work, we apply all-electron phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) utilizing multideterminant trial wave functions to six metallocene complexes to compare the computed adiabatic and vertical ionization energies with experimental results. We find that ph-AFQMC yields mean absolute errors (MAEs) of 1.69 ± 1.02 kcal/mol for the adiabatic energies and 2.85 ± 1.13 kcal/mol for the vertical energies. We also carry out density functional theory (DFT) calculations using a variety of functionals, which yields MAEs of 3.62-6.98 kcal/mol and 3.31-9.88 kcal/mol, as well as one variant of localized coupled cluster calculations (DLPNO-CCSD(T0) with moderate PNO cutoffs), which has MAEs of 4.96 and 6.08 kcal/mol, respectively. We also test the reliability of DLPNO-CCSD(T0) and DFT on acetylacetonate (acac) complexes for adiabatic energies measured in the same manner experimentally, and we find higher MAEs, ranging from 4.56 to 10.99 kcal/mol (with a different ordering) for DFT and 6.97 kcal/mol for DLPNO-CCSD(T0). Finally, by utilizing experimental solvation energies, we show that accurate reduction potentials in solution for the metallocene series can be obtained from the AFQMC gas phase results.

Molecular Engineering of Chromophores to Enable Triplet-Triplet Annihilation Upconversion.

Triplet-triplet annihilation upconversion (TTA-UC) is an unconventional photophysical process that yields high-energy photons from low-energy incident light and offers pathways for innovation across many technologies, including solar energy harvesting, photochemistry, and optogenetics. Within aromatic organic chromophores, TTA-UC is achieved through several consecutive energy conversion events that ultimately fuse two triplet excitons into a singlet exciton. In chromophores where the singlet exciton is roughly isoergic with two triplet excitons, the limiting step is the triplet-triplet annihilation pathway, where the kinetics and yield depend sensitively on the energies of the lowest singlet and triplet excited states. Herein we report up to 40-fold improvements in upconversion quantum yields using molecular engineering to selectively tailor the relative energies of the lowest singlet and triplet excited states, enhancing the yield of triplet-triplet annihilation and promoting radiative decay of the resulting singlet exciton. Using this general and effective strategy, we obtain upconversion yields with red emission that are among the highest reported, with remarkable chemical stability under ambient conditions.

Predicting Ligand-Dissociation Energies of 3d Coordination Complexes with Auxiliary-Field Quantum Monte Carlo.

Transition-metal complexes are ubiquitous in biology and chemical catalysis, yet they remain difficult to accurately describe with ab initio methods because of the presence of a large degree of dynamic electron correlation, and, in some cases, strong static correlation which results from a manifold of low-lying states. Progress has been hindered by a scarcity of high-quality gas-phase experimental data, while exact ab initio predictions are usually computationally unaffordable because of the large size of the relevant complexes. In this work, we present a data set of 34 tetrahedral, square planar, and octahedral 3d metal-containing complexes with gas-phase ligand-dissociation energies that have reported uncertainties of ≤2 kcal/mol. We perform all-electron phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) calculations utilizing multideterminant trial wave functions selected by a black box procedure. We compare the results with those from the density functional theory (DFT) with the B3LYP, B97, M06, PBE0, ωB97X-V, and DSD-PBEP86/2013 functionals and a localized orbital variant of the coupled cluster theory with single, double, and perturbative triple excitations (DLPNO-CCSD(T)). We find mean averaged errors of 1.07 ± 0.27 kcal/mol for our most sophisticated ph-AFQMC approach versus 2.81 kcal/mol for DLPNO-CCSD(T) and 1.49-3.78 kcal/mol for DFT. We find maximum errors of 2.96 ± 1.71 kcal/mol for our best ph-AFQMC method versus 9.15 kcal/mol for DLPNO-CCSD(T) and 5.98-13.69 kcal/mol for DFT. The reasonable performance of a number of DFT functionals is in stark contrast to the much poorer accuracy previously demonstrated for diatomic species, suggesting a moderation in electron correlation because of ligand coordination in most cases. However, the unpredictably large errors for a small subset of cases with both DFT and DLPNO-CCSD(T) methods leave cause for concern, especially in light of the unreliability of common multireference indicators. In contrast, the robust and, in principle, systematically improvable results of ph-AFQMC for these realistic complexes establish the method as a useful tool for elucidating the electronic structure of transition-metal-containing complexes and predicting their gas-phase properties.

Accurate Quantum Chemical Calculation of Ionization Potentials: Validation of the DFT-LOC Approach via a Large Data Set Obtained from Experiments and Benchmark Quantum Chemical Calculations.

Density functional theory (DFT) is known to often fail when calculating thermodynamic values, such as ionization potentials (IPs), due to nondynamical error (i.e., the self-interaction term). Localized orbital corrections (LOCs), derived from assigning corresponding corrections for the atomic orbitals, bonds, and paired and unpaired electrons, are utilized to correct the IPs calculated from DFT. Some of the assigned parameters, which are physically due to the contraction of and change of the environment around a bond, depend on identifying the location in the molecule from which the electron is removed using differences in the charge density between neutral and oxidized species. In our training set, various small organic and inorganic molecules from the literature with the reported experimental IP were collected using the NIST database. For certain molecules with uncertain or no experimental measurements, we obtain the IP using coupled cluster theory and auxiliary field quantum Monte Carlo. After applying these corrections, as generated by least-squares regression, LOC reduces the mean absolute deviation (MAD) of the training set from 0.143 to 0.046 eV (R2 = 0.895), and LOC reduces the MAD of the test set from 0.192 to 0.097 eV (R2 = 0.833).

In silico prediction of annihilators for triplet-triplet annihilation upconversion via auxiliary-field quantum Monte Carlo.

The energy of the lowest-lying triplet state (T1) relative to the ground and first-excited singlet states (S0, S1) plays a critical role in optical multiexcitonic processes of organic chromophores. Focusing on triplet-triplet annihilation (TTA) upconversion, the S0 to T1 energy gap, known as the triplet energy, is difficult to measure experimentally for most molecules of interest. Ab initio predictions can provide a useful alternative, however low-scaling electronic structure methods such as the Kohn-Sham and time-dependent variants of Density Functional Theory (DFT) rely heavily on the fraction of exact exchange chosen for a given functional, and tend to be unreliable when strong electronic correlation is present. Here, we use auxiliary-field quantum Monte Carlo (AFQMC), a scalable electronic structure method capable of accurately describing even strongly correlated molecules, to predict the triplet energies for a series of candidate annihilators for TTA upconversion, including 9,10 substituted anthracenes and substituted benzothiadiazole (BTD) and benzoselenodiazole (BSeD) compounds. We compare our results to predictions from a number of commonly used DFT functionals, as well as DLPNO-CCSD(T0), a localized approximation to coupled cluster with singles, doubles, and perturbative triples. Together with S1 estimates from absorption/emission spectra, which are well-reproduced by TD-DFT calculations employing the range-corrected hybrid functional CAM-B3LYP, we provide predictions regarding the thermodynamic feasibility of upconversion by requiring (a) the measured T1 of the sensitizer exceeds that of the calculated T1 of the candidate annihilator, and (b) twice the T1 of the annihilator exceeds its S1 energetic value. We demonstrate a successful example of in silico discovery of a novel annihilator, phenyl-substituted BTD, and present experimental validation via low temperature phosphorescence and the presence of upconverted blue light emission when coupled to a platinum octaethylporphyrin (PtOEP) sensitizer. The BTD framework thus represents a new class of annihilators for TTA upconversion. Its chemical functionalization, guided by the computational tools utilized herein, provides a promising route towards high energy (violet to near-UV) emission.