Optimization of the linear-scaling local natural orbital CCSD(T) method: Redundancy-free triples correction using Laplace transform

Assessing the domain-based local pair natural orbital (DLPNO) approximation for non-covalent interactions in sizable supramolecular complexes

The titular domain-based local pair natural orbital (DLPNO) approximation is the most widely used method for extending correlated wave function models to large molecular systems, yet its fidelity for intermolecular interaction energies in large supramolecular complexes has not been thoroughly vetted. Non-covalent interactions are sensitive to tails of the electron density and involve nonlocal dispersion that is discarded or approximated if the screening of pair natural orbitals (PNOs) is too aggressive. Meanwhile, the accuracy of the DLPNO approximation is known to deteriorate as molecular size increases. Here, we test the DLPNO approximation at the level of second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster theory with singles, doubles, and perturbative triples [CCSD(T)] for a variety of large supramolecular complexes. DLPNO-MP2 interaction energies are within 3% of canonical values for small dimers with ≲10 heavy atoms, but for larger systems, the DLPNO approximation is often quite poor unless the results are extrapolated to the canonical limit where the threshold for discarding PNOs is taken to zero. Counterpoise correction proves to be essential in reducing errors with respect to canonical results. For a sequence of nanoscale graphene dimers up to (C96H24)2, extrapolated DLPNO-MP2 interaction energies agree with canonical values to within 1%, independent of system size, provided that the basis set does not contain diffuse functions; these cause the DLPNO approximation to behave erratically, such that results cannot be extrapolated in a meaningful way. DLPNO-CCSD(T) calculations are typically performed using looser PNO thresholds as compared to DLPNO-MP2, but this significantly impacts accuracy for large supramolecular complexes. Standard DLPNO-CCSD(T) settings afford errors of 2-6 kcal/mol for dimers involving coronene (C24H12) and circumcoronene (C54H18), even at the DLPNO-CCSD(T1) level.

The p-block challenge: assessing quantum chemistry methods for inorganic heterocycle dimerizations

The elements of the p-block of the periodic table are of high interest in various chemical and technical applications like frustrated Lewis-pairs (FLP) or opto-electronics. However, high-quality benchmark data to assess approximate density functional theory (DFT) for their theoretical description are sparse. In this work, we present a benchmark set of 604 dimerization energies of 302 "inorganic benzenes" composed of all non-carbon p-block elements of main groups III to VI up to polonium. This so-called IHD302 test set comprises two classes of structures formed by covalent bonding and by weaker donor-acceptor (WDA) interactions, respectively. Generating reliable reference data with ab initio methods is challenging due to large electron correlation contributions, core-valence correlation effects, and especially the slow basis set convergence. To compute reference values for these dimerization reactions, after thorough testing, we applied a computational protocol using state-of-the-art explicitly correlated local coupled cluster theory termed PNO-LCCSD(T)-F12/cc-VTZ-PP-F12(corr.). It includes a basis set correction at the PNO-LMP2-F12/aug-cc-pwCVTZ level. Based on these reference data, we assess 26 DFT methods in combination with three different dispersion corrections and the def2-QZVPP basis set, five composite DFT approaches, and five semi-empirical quantum mechanical methods. For the covalent dimerizations, the r2SCAN-D4 meta-GGA, the r2SCAN0-D4 and ωB97M-V hybrids, and the revDSD-PBEP86-D4 double-hybrid functional are found to be the best-performing methods among the evaluated functionals of the respective class. However, since def2 basis sets for the 4th period are not associated to relativistic pseudo-potentials, we obtained significant errors in the covalent dimerization energies (up to 6 kcal mol-1) for molecules containing p-block elements of the 4th period. Significant improvements were achieved for systems containing 4th row elements by using ECP10MDF pseudopotentials along with re-contracted aug-cc-pVQZ-PP-KS basis sets introduced in this work with the contraction coefficients taken from atomic DFT (PBE0) calculations. Overall, the IHD302 set represents a challenge to contemporary quantum chemical methods. This is due to a large number of spatially close p-element bonds which are underrepresented in other benchmark sets, and the partial covalent bonding character for the WDA interactions. The IHD302 set may be helpful to develop more robust and transferable approximate quantum chemical methods in the future.

W4Λ: Leveraging Λ Coupled-Cluster for Accurate Computational Thermochemistry Approaches

High-accuracy composite wave function methods like Weizmann-4 (W4) theory, high-accuracy extrapolated ab initio thermochemistry (HEAT), and the Feller-Peterson-Dixon (FPD) approach enable sub-kJ/mol accuracy in gas-phase thermochemical properties. Their biggest computational bottleneck is the evaluation of the valence post-CCSD(T) correction term. We demonstrate here, for the W4-17 thermochemistry benchmark and subsets thereof, that the Λ coupled-cluster expansion converges more rapidly and smoothly than the regular coupled-cluster series. By means of CCSDT(Q)Λ and CCSDTQ(5)Λ, we can considerably (up to an order of magnitude) accelerate W4- and W4.3-type calculations without loss in accuracy, leading to the W4Λ and W4.3Λ computational thermochemistry protocols.

Formation Enthalpies of C3 and C4 Brominated Hydrocarbons: Bringing Together Classical Thermodynamics, Modern Mass Spectrometry, and High-Level Ab Initio Calculations

The enthalpies of formation of brominated C3-C4 hydrocarbons were critically evaluated using experimental data sources ranging from classical thermodynamics methods to modern high-precision mass spectrometry and reported in a time span of a century. The experimental data were used in conjunction with the results of modern high-level ab initio calculations. To facilitate quantitative analysis, a recently developed local coupled cluster-based computational protocol was extended to organic compounds containing univalent Br. Several erroneous data sources were identified in a course of the study. Possible reasons for the inconsistency between the ΔfHm° values recommended by the Committee on Data of the International Science Council (CODATA) and Active Thermochemical Tables for HBr in the gas and aqueous solution were discussed. The most up-to-date recommendations based on the comprehensive analysis of collected information are provided for 23 brominated hydrocarbons. For several compounds under consideration, the recommended values were previously lacking, while improved values and uncertainties were obtained for those with existing recommendations.

Cholesky Decomposition-Based Implementation of Relativistic Two-Component Coupled-Cluster Methods for Medium-Sized Molecules

A Cholesky decomposition (CD)-based implementation of relativistic two-component coupled-cluster (CC) and equation-of-motion CC (EOM-CC) methods using an exact two-component Hamiltonian augmented with atomic-mean-field spin-orbit integrals (the X2CAMF scheme) is reported. The present CD-based implementation of X2CAMF-CC and EOM-CC methods employs atomic-orbital-based algorithms to avoid the construction of two-electron integrals and intermediates involving three and four virtual indices. Our CD-based implementation extends the applicability of X2CAMF-CC and EOM-CC methods to medium-sized molecules with the possibility to correlate around 1000 spinors. Benchmark calculations for uranium-containing small molecules were performed to assess the dependence of the CC results on the Cholesky threshold. A Cholesky threshold of 10-4 is shown to be sufficient to maintain chemical accuracy. Example calculations to illustrate the capability of the CD-based relativistic CC methods are reported for the bond-dissociation energy of the uranium hexafluoride molecule, UF6, with up to quadruple-ζ basis sets, and the lowest excitation energy in the solvated uranyl ion [UO22+(H2O)12].

Polarizable AMOEBA Model for Simulating Mg2+·Protein·Nucleotide Complexes

Molecular mechanics (MM) simulations have the potential to provide detailed insights into the mechanisms of enzymes that utilize nucleotides as cofactors. In most cases, the activities of these enzymes also require the binding of divalent cations to catalytic sites. However, modeling divalent cations in MM simulations has been challenging. The inclusion of explicit polarization was considered promising, but despite improvements over nonpolarizable force fields and despite the inclusion of "Nonbonded-fix (NB-fix)" corrections, errors in interaction energies of divalent cations with proteins remain large. Importantly, the application of these models fails to reproduce the experimental structural data on Mg2+·Protein·ATP complexes. Focusing on these complexes, here we provide a systematic assessment of the polarizable AMOEBA model and recommend critical changes that substantially improve its predictive performance. Our key results are as follows. We first show that our recent revision of the AMOEBA protein model (AMOEBABIO18-HFC), which contains high field corrections (HFCs) to induced dipoles, dramatically improves Mg2+-protein interaction energies, reducing the mean absolute error (MAE) from 17 to 10 kcal/mol. This further supports the general applicability of AMOEBABIO18-HFC. The inclusion of many-body NB-fix corrections further reduces MAE to 6 kcal/mol, which amounts to less than 2% error. The errors are estimated with respect to vdW-inclusive density functional theory that we benchmark against CCSD(T) calculations and experiments. We also present a new model of ATP with revised polarization parameters to better capture its high field response, as well as new vdW and dihedral parameters. The ATP model accurately predicts experimental Mg2+-ATP binding free energy in the aqueous phase and provides new insights into how Mg2+ associates with ATP. Finally, we show that molecular dynamics (MD) simulations of Mg2+·Kinase·ATP complexes carried out with these improvements lead to a better agreement in global and local catalytic site structures between MD and X-ray crystallography.

Toward Linear Scaling Auxiliary-Field Quantum Monte Carlo with Local Natural Orbitals

We develop a local correlation variant of auxiliary-field quantum Monte Carlo (AFQMC) based on local natural orbitals (LNO-AFQMC). In LNO-AFQMC, independent AFQMC calculations are performed for each localized occupied orbital using a truncated set of tailored orbitals. Because the size of this space does not grow with the system size for a target accuracy, the method has linear scaling. Applying LNO-AFQMC to molecular problems containing a few hundred to a thousand orbitals, we demonstrate convergence of total energies with significantly reduced costs. The savings are more significant for larger systems and larger basis sets. However, even for our smallest system studied, we find that LNO-AFQMC is cheaper than canonical AFQMC, in contrast with many other reduced-scaling methods. Perhaps most significantly, we show that energy differences converge much more quickly than total energies, making the method ideal for applications in chemistry and material science. Our work paves the way for linear scaling AFQMC calculations of strongly correlated systems, which would have a transformative effect on ab initio quantum chemistry.

Linear-Scaling Local Natural Orbital CCSD(T) Approach for Open-Shell Systems: Algorithms, Benchmarks, and Large-Scale Applications

The extension of the highly optimized local natural orbital (LNO) coupled cluster (CC) with single-, double-, and perturbative triple excitations [LNO-CCSD(T)] method is presented for high-spin open-shell molecules based on restricted open-shell references. The techniques enabling the outstanding efficiency of the closed-shell LNO-CCSD(T) variant are adopted, including the iteration- and redundancy-free second-order Møller-Plesset and (T) formulations as well as the integral-direct, memory- and disk use-economic, and OpenMP-parallel algorithms. For large molecules, the efficiency of our open-shell LNO-CCSD(T) method approaches that of its closed-shell parent method due to the application of restricted orbital sets for demanding integral transformations and a novel approximation for higher-order long-range spin-polarization effects. The accuracy of open-shell LNO-CCSD(T) is extensively tested for radicals and reactions thereof, ionization processes, as well as spin-state splittings, and transition-metal compounds. At the size range where the canonical CCSD(T) reference is accessible (up to 20-30 atoms), the average open-shell LNO-CCSD(T) correlation energies are found to be 99.9 to 99.95% accurate, which translates into average absolute deviations of a few tenths of kcal/mol in the investigated energy differences already with the default settings. For more extensive molecules, the local errors may grow, but they can be estimated and decreased via affordable systematic convergence studies. This enables the accurate modeling of large systems with complex electronic structures, as illustrated on open-shell organic radicals and transition-metal complexes of up to 179 atoms as well as on challenging biochemical systems, including up to 601 atoms and 11,000 basis functions. While the protein models involve difficulties for local approximations, such as the spin states of a bounded iron ion or an extremely delocalized singly occupied orbital, the corresponding single-node LNO-CCSD(T) computations were feasible in a matter of days with 10s to 100 GB of memory use. Therefore, the new LNO-CCSD(T) implementation enables highly accurate computations for open-shell systems of unprecedented size and complexity with widely accessible hardware.

Cluster-in-Molecule Approach with Explicitly Correlated Methods for Large Molecules

In this article, we present a series of explicitly correlated local correlation methods developed under the cluster-in-molecule (CIM) framework, including explicitly correlated second-order Møller-Plesset perturbation (MP2), coupled-cluster singles and doubles (CCSD), domain-based local pair natural orbital CCSD (DLPNO-CCSD), and DLPNO-CCSD with perturbative triples (DLPNO-CCSD(T)). In these methods, F12 correction is decomposed into contributions from each occupied local molecular orbital and then evaluated independently in a given cluster, which consists of a subset of localized orbitals. These newly developed methods allow F12 calculations of large molecules (up to 145 atoms for quasi-one-dimensional systems) on a single node. We use these methods to investigate the relative stability between extended and folded alkane C30H62, the relative stability of four secondary structures of a polyglycine Ace(Gly)10NH2, and the binding energies of two host-guest complexes. The results demonstrate that the combination of CIM with F12 methods is a promising way to investigate large molecules with small basis set errors.

Many-Body Methods for Surface Chemistry Come of Age: Achieving Consensus with Experiments

The adsorption energy of a molecule onto the surface of a material underpins a wide array of applications, spanning heterogeneous catalysis, gas storage, and many more. It is the key quantity where experimental measurements and theoretical calculations meet, with agreement being necessary for reliable predictions of chemical reaction rates and mechanisms. The prototypical molecule-surface system is CO adsorbed on MgO, but despite intense scrutiny from theory and experiment, there is still no consensus on its adsorption energy. In particular, the large cost of accurate many-body methods makes reaching converged theoretical estimates difficult, generating a wide range of values. In this work, we address this challenge, leveraging the latest advances in diffusion Monte Carlo (DMC) and coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] to obtain accurate predictions for CO on MgO. These reliable theoretical estimates allow us to evaluate the inconsistencies in published temperature-programed desorption experiments, revealing that they arise from variations in employed pre-exponential factors. Utilizing this insight, we derive new experimental estimates of the (electronic) adsorption energy with a (more) precise pre-exponential factor. As a culmination of all of this effort, we are able to reach a consensus between multiple theoretical calculations and multiple experiments for the first time. In addition, we show that our recently developed cluster-based CCSD(T) approach provides a low-cost route toward achieving accurate adsorption energies. This sets the stage for affordable and reliable theoretical predictions of chemical reactions on surfaces to guide the realization of new catalysts and gas storage materials.

Accurate Calculation of Isomerization and Conformational Energies of Larger Molecules Using Explicitly Correlated Local Coupled Cluster Methods in Molpro and ORCA

An overview of the approximations in the explicitly correlated local coupled cluster methods PNO-LCCSD(T)-F12 in Molpro and DLPNO-CCSD(T)F12 in ORCA is given. Options to select the domains of projected atomic orbitals (PAOs), pair natural orbitals (PNOs), and triples natural orbitals (TNOs) in both programs are described and compared in detail. The two programs are applied to compute isomerization and conformational energies of the ISOL24 and ACONFL test sets, where the former is part of the GMTKN55 benchmark suite. Thorough studies of basis set effects are presented for selected systems. These revealed large intramolecular basis set superposition effects that make it practically impossible to reliably determine the complete basis set (CBS) limits without including explicitly correlated terms. The latter strongly reduce the basis set dependence and at the same time also errors caused by the local domain approximations. On the basis of these studies, the PNO-LCCSD(T)-F12 method is applied to determine new reference energies for the above-mentioned benchmark sets. We are confident that our results should agree within a few tenths of a kcal mol-1 with the (unknown) CCSD(T)/CBS values, which therefore allowed us to define computational settings for accurate explicitly correlated local coupled cluster methods with moderate computational effort. With these protocols, especially PNO-LCCSD(T)-F12b/AVTZ', reliable reference values for comprehensive benchmark sets can be generated efficiently. This can significantly advance the development and evaluation of the performance of approximate electronic structure methods, especially improved density functional approximations or machine learning approaches.

Correlation Consistent Basis Sets for Explicitly Correlated Theory: The Transition Metals

We present correlation consistent basis sets for explicitly correlated (F12) calculations, denoted VnZ(-PP)-F12-wis (n = D,T), for the d-block elements. The cc-pVDZ-F12-wis basis set is contracted to [8s7p5d2f] for the 3d-block, while its ECP counterpart for the 4d and 5d-blocks, cc-pVDZ-PP-F12-wis, is contracted to [6s6p5d2f]. The corresponding contracted sizes for cc-pVTZ(-PP)-F12-wis are [9s8p6d3f2g] for the 3d-block elements and [7s7p6d3f2g] for the 4d and 5d-block elements. Our VnZ(-PP)-F12-wis basis sets are evaluated on challenging test sets for metal-organic barrier heights (MOBH35) and group-11 metal clusters (CUAGAU-2). In F12 calculations, they are found to be about as close to the complete basis set limit as the combination of standard cc-pVnZ-F12 on main-group elements with the standard aug-cc-pV(n+1)Z(-PP) basis sets on the transition metal(s). While our basis sets are somewhat more compact than aug-cc-pV(n+1)Z(-PP), the CPU time benefit is negligible for catalytic complexes that contain only one or two transition metals among dozens of main-group elements; however, it is somewhat more significant for metal clusters.

Toward Pair Atomic Density Fitting for Correlation Energies with Benchmark Accuracy

Pair atomic density fitting (PADF) has been identified as a promising strategy to reduce the scaling with system size of quantum chemical methods for the calculation of the correlation energy like the direct random-phase approximation (RPA) or second-order Møller-Plesset perturbation theory (MP2). PADF can however introduce large errors in correlation energies as the two-electron interaction energy is not guaranteed to be bounded from below. This issue can be partially alleviated by using very large fit sets, but this comes at the price of reduced efficiency and having to deal with near-linear dependencies in the fit set. One posibility is to use global density fitting (DF), but in this work, we introduce an alternative methodology to overcome this problem that preserves the intrinsically favorable scaling of PADF. We first regularize the Fock matrix by projecting out parts of the basis set which gives rise to orbital products that are hard to describe by PADF. After having thus obtained a reliable self-consistent field solution, we then also apply this projector to the orbital coefficient matrix to improve the precision of PADF-MP2 and PADF-RPA. We systematically assess the accuracy of this new approach in a numerical atomic orbital framework using Slater type orbitals (STO) and correlation consistent Gaussian type basis sets up to quintuple-ζ quality for systems with more than 200 atoms. For the small and medium systems in the S66 database we show the maximum deviation of PADF-MP2 and PADF-RPA relative correlation energies to DF-MP2 and DF-RPA reference results to be 0.07 and 0.14 kcal/mol, respectively. When the new projector method is used, the errors only slightly increase for large molecules and also when moderately sized fit sets are used the resulting errors are well under control. Finally, we demonstrate the computational efficiency of our algorithm by calculating the interaction energies of large, non-covalently bound complexes with more than 1000 atoms and 20000 atomic orbitals at the RPA@PBE/CC-pVTZ level of theory.

Are Accelerated and Enhanced Wave Function Methods Accurate to Compute Static Linear and Nonlinear Optical Properties?

Key components of organic-based electro-optic devices are challenging to design or optimize because they exhibit nonlinear optical responses, which are difficult to model or rationalize. Computational chemistry furnishes the tools to investigate extensive collections of molecules in the quest for target compounds. Among the electronic structure methods that provide static nonlinear optical properties (SNLOPs), density functional approximations (DFAs) are often preferred because of their low cost/accuracy ratio. However, the accuracy of the SNLOPs critically depends on the amount of exact exchange and electron correlation included in the DFA, precluding the reliable calculation of many molecular systems. In this scenario, wave function methods such as MP2, CCSD, and CCSD(T) constitute a reliable alternative to compute SNLOPs. Unfortunately, the computational cost of these methods significantly restricts the size of molecules to study, a limitation that hampers the identification of molecules with significant nonlinear optical responses. This paper analyzes various flavors and alternatives to MP2, CCSD, and CCSD(T) methods that either drastically reduce the computational cost or improve their performance but were scarcely and unsystematically employed to compute SNLOPs. In particular, we have tested RI-MP2, RIJK-MP2, RIJCOSX-MP2 (with GridX2 and GridX4 setups), LMP2, SCS-MP2, SOS-MP2, DLPNO-MP2, LNO-CCSD, LNO-CCSD(T), DLPNO-CCSD, DLPNO-CCSD(T0), and DLPNO-CCSD(T1). Our results indicate that all these methods can be safely employed to calculate the dipole moment and the polarizability with average relative errors below 5% with respect to CCSD(T). On the other hand, the calculation of higher-order properties represents a challenge for LNO and DLPNO methods, which present severe numerical instabilities in computing the single-point field-dependent energies. RI-MP2, RIJK-MP2, or RIJCOSX-MP2 are cost-effective methods to compute first and second hyperpolarizabilities with a marginal average error with respect to canonical MP2 (up to 5% for β and up to 11% for γ). More accurate hyperpolarizabilities can be obtained with DLPNO-CCSD(T1); however, this method cannot be employed to obtain reliable second hyperpolarizabilities. These results open the way to obtain accurate nonlinear optical properties at a computational cost that can compete with current DFAs.

Molecular Understanding and Practical In Silico Catalyst Design in Computational Organocatalysis and Phase Transfer Catalysis-Challenges and Opportunities

Through the lens of organocatalysis and phase transfer catalysis, we will examine the key components to calculate or predict catalysis-performance metrics, such as turnover frequency and measurement of stereoselectivity, via computational chemistry. The state-of-the-art tools available to calculate potential energy and, consequently, free energy, together with their caveats, will be discussed via examples from the literature. Through various examples from organocatalysis and phase transfer catalysis, we will highlight the challenges related to the mechanism, transition state theory, and solvation involved in translating calculated barriers to the turnover frequency or a metric of stereoselectivity. Examples in the literature that validated their theoretical models will be showcased. Lastly, the relevance and opportunity afforded by machine learning will be discussed.

Performance of Localized-Orbital Coupled-Cluster Approaches for the Conformational Energies of Longer n-Alkane Chains

We report an update and enhancement of the ACONFL (conformer energies of large alkanes [J. Phys. Chem. A2022,126, 3521-3535]) dataset. For the ACONF12 (n-dodecane) subset, we report basis set limit canonical coupled-cluster with singles, doubles, and perturbative triples [i.e., CCSD(T)] reference data obtained from the MP2-F12/cc-pV{T,Q}Z-F12 extrapolation, [CCSD(F12*)-MP2-F12]/aug-cc-pVTZ-F12, and a (T) correction from conventional CCSD(T)/aug-cc-pV{D,T}Z calculations. Then, we explored the performance of a variety of single and composite localized-orbital CCSD(T) approximations, ultimately finding an affordable localized natural orbital CCSD(T) [LNO-CCSD(T)]-based post-MP2 correction that agrees to 0.006 kcal/mol mean absolute deviation with the revised canonical reference data. In tandem with canonical MP2-F12 complete basis set extrapolation, this was then used to re-evaluate the ACONF16 and ACONF20 subsets for n-hexadecane and n-icosane, respectively. Combining those with the revised canonical reference data for the dodecane conformers (i.e., ACONF12 subset), a revised ACONFL set was obtained. It was then used to assess the performance of different localized-orbital coupled-cluster approaches, such as pair natural orbital localized CCSD(T) [PNO-LCCSD(T)] as implemented in MOLPRO, DLPNO-CCSD(T₀) and DLPNO-CCSD(T₁) as implemented in ORCA, and LNO-CCSD(T) as implemented in MRCC, at their respective "Normal", "Tight", "vTight", and "vvTight" accuracy settings. For a given accuracy threshold and basis set, DLPNO-CCSD(T₁) and DLPNO-CCSD(T₀) perform comparably. With "VeryTightPNO" cutoffs, explicitly correlated DLPNO-CCSD(T₁)-F12/VDZ-F12 is the best pick among all the DLPNO-based methods tested. To isolate basis set incompleteness from localized-orbital-related truncation errors (domain, LNOs), we have also compared the localized coupled-cluster approaches with canonical DF-CCSD(T)/aug-cc-pVTZ for the ACONF12 set. We found that gradually tightening the cutoffs improves the performance of LNO-CCSD(T), and using a composite scheme such as vTight + 0.50[vTight - Tight] improves things further. For DLPNO-CCSD(T₁), "TightPNO" and "VeryTightPNO" offer a statistically similar accuracy, which gets slightly better when T_CutPNO is extrapolated to the complete PNO space limit. Similar to Brauer et al.'s [Phys. Chem. Chem. Phys.2016,18 (31), 20905-20925] previous report for the S66x8 noncovalent interactions, the dispersion-corrected direct random phase approximation (dRPA)-based double hybrids perform remarkably well for the ACONFL set. While the revised reference data do not affect any conclusions on the less accurate methods, they may upend orderings for more accurate methods with error statistics on the same order as the difference between reference datasets.

Cluster-in-Molecule Method Combined with the Domain-Based Local Pair Natural Orbital Approach for Electron Correlation Calculations of Periodic Systems

The cluster-in-molecule (CIM) method was extended to systems with periodic boundary conditions (PBCs) in a previous work (PBC-CIM) [J. Chem. Theory Comput.2019, 15, 2933], which is able to compute the electronic structures of periodic systems at second-order Møller-Plesset perturbation theory (MP2) and coupled cluster singles and doubles (CCSD) levels. However, the high computational costs of CCSD with respect to the size of clusters limit the usage of PBC-CIM to crystals with small or medium unit cells. In this work, we further develop the PBC-CIM method by employing the domain-based local pair natural orbital (DLPNO) methods for the electron correlation calculations of clusters to reduce the computational costs. The combined approach allows CCSD with perturbative triples, denoted as CCSD(T), to be computationally available for accurate descriptions of periodic systems. The distant-pair correction is also implemented to improve the accuracy of PBC-CIM. As in the molecular cases, the distant pair correction significantly improves the accuracy of various PBC-CIM methods with few additional costs. The PBC-CIM-DLPNO-CCSD(T) approach has been applied to investigate the optimized lattice parameter of the cubic LiCl crystal and two adsorption problems (CO on the NaCl(100) surface and H₂O on the h-BN surface). The results show that the CIM-DLPNO-CCSD(T) method offers accurate and efficient descriptions for the studied systems. Another application to the cohesive energy of the acetic acid crystal reveals that large basis sets are necessary for reliable calculations on the cohesive energies of molecular crystals.

Stability of Carbocyclic Phosphinyl Radicals: Effect of Ring Size, Delocalization, and Sterics

In this computational study, we report on the stability of cyclic phosphinyl radicals with an aim for a systematical assessment of stabilization effects. The radical stabilization energies (RSEs) were calculated using isodesmic reactions for a large number of carbocyclic radicals possessing different ring sizes and grades of unsaturation. In general, the RSE values range from −1.2 to −14.0 kcal·mol^–1, and they show practically no correlation with the spin populations at the P-centers. The RSE values correlate with the reaction Gibbs free energies calculated for the dimerization of the studied simple radicals. Therefore, the more easily accessible RSE values offer a cost-effective estimation of global stability in a straightforward manner. To explore the effect of unsaturation on the RSE values, delocalization energies were determined using appropriate isodesmic reactions. Introducing unsaturations beside the P-center into the backbone of the rings leads to an additive increase in the magnitude of the delocalization energy (∼10, 20, and 30 kcal·mol^–1, respectively, for radicals with one, two, and three C=C bonds in the conjugation). Parallelly, the spin populations at the P-centers also dwindle gradually by ∼0.1 e in the same order, indicating that the lone electron delocalizes over the π-system. Radicals containing exocyclic C=C π-bonds were also investigated, and all of these radicals have rather similar stabilities independently of the ring size, outlining the primary importance of the two exocyclic π-bonds in the conjugation. Among the radicals involved in our study, those with the best electronic stabilization are the unsaturated three-, five-, six-, and seven-membered rings containing the maximum number of conjugated vinyl fragments. The largest delocalization energy of 31.5 kcal·mol^–1 and the lowest obtained spin population of 0.665 e were found for the fully unsaturated seven-membered radical (phosphepin derivative). Importantly, the electronic stabilization effects alone are insufficient for stabilizing the radicals in monomeric forms epitomized by the exothermic dimerization energies (−40 to −58 kcal·mol^–1). Therefore, it is essential to apply sterically demanding bulky substituents on the α-C-atoms. Tweaking the steric congestion enabled us to propose radicals that are expected to be stable against dimerization and, consequently, may be realistic target species for synthetic investigations. The effects contributing to the stability of radicals having sterically encumbered substituents have also been explored.

To systematically evaluate the stabilization effects, the radical stabilization energies of various carbocyclic phosphinyl radicals having saturated backbones or unsaturation(s) in either endocyclic or exocyclic manner have been determined and analyzed. As the electronic stabilization is alone insufficient to hamper the possible dimerization of these species, the effect of several sterically demanding substituents has been explored for the congeners with best electronic stabilizations, thus enabling us to propose synthetically accessible candidates in the future.

General embedded cluster protocol for accurate modeling of oxygen vacancies in metal-oxides

The O vacancy (Ov) formation energy, EOv, is an important property of a metal-oxide, governing its performance in applications such as fuel cells or heterogeneous catalysis. These defects are routinely studied with density functional theory (DFT). However, it is well-recognized that standard DFT formulations (e.g., the generalized gradient approximation) are insufficient for modeling the Ov, requiring higher levels of theory. The embedded cluster method offers a promising approach to compute EOv accurately, giving access to all electronic structure methods. Central to this approach is the construction of quantum(-mechanically treated) clusters placed within suitable embedding environments. Unfortunately, current approaches to constructing the quantum clusters either require large system sizes, preventing application of high-level methods, or require significant manual input, preventing investigations of multiple systems simultaneously. In this work, we present a systematic and general quantum cluster design protocol that can determine small converged quantum clusters for studying the Ov in metal-oxides with accurate methods, such as local coupled cluster with single, double, and perturbative triple excitations. We apply this protocol to study the Ov in the bulk and surface planes of rutile TiO2 and rock salt MgO, producing the first accurate and well-converged determinations of EOv with this method. These reference values are used to benchmark exchange–correlation functionals in DFT, and we find that all the studied functionals underestimate EOv, with the average error decreasing along the rungs of Jacob’s ladder. This protocol is automatable for high-throughput calculations and can be generalized to study other point defects or adsorbates.

The MOBH35 Metal–Organic Barrier Heights Reconsidered: Performance of Local-Orbital Coupled Cluster Approaches in Different Static Correlation Regimes

We have revisited the MOBH35 (Metal–Organic Barrier Heights, 35 reactions) benchmark [Iron, Janes, J. Phys. Chem. A, 2019, 123 ( (17), ), 3761−378130973722; ibid. 2019, 123, 6379–6380] for realistic organometallic catalytic reactions, using both canonical CCSD(T) and localized orbital approximations to it. For low levels of static correlation, all of DLPNO-CCSD(T), PNO-LCCSD(T), and LNO-CCSD(T) perform well; for moderately strong levels of static correlation, DLPNO-CCSD(T) and (T₁) may break down catastrophically, and PNO-LCCSD(T) is vulnerable as well. In contrast, LNO-CCSD(T) converges smoothly to the canonical CCSD(T) answer with increasingly tight convergence settings. The only two reactions for which our revised MOBH35 reference values differ substantially from the original ones are reaction 9 and to a lesser extent 8, both involving iron. For the purpose of evaluating density functional theory (DFT) methods for MOBH35, it would be best to remove reaction 9 entirely as its severe level of static correlation makes it just too demanding for a test. The magnitude of the difference between DLPNO-CCSD(T) and DLPNO-CCSD(T₁) is a reasonably good predictor for errors in DLPNO-CCSD(T₁) compared to canonical CCSD(T); otherwise, monitoring all of T₁, D₁, max|t_i^A|, and 1/(ε_LUMO – ε_HOMO) should provide adequate warning for potential problems. Our conclusions are not specific to the def2-SVP basis set but are largely conserved for the larger def2-TZVPP, as they are for the smaller def2-SV(P): the latter may be an economical choice for calibrating against canonical CCSD(T). Finally, diagnostics for static correlation are statistically clustered into groups corresponding to (1) importance of single excitations in the wavefunction; (2a) the small band gap, weakly separated from (2b) correlation entropy; and (3) thermochemical importance of correlation energy, as well as the slope of the DFT reaction energy with respect to the percentage of HF exchange. Finally, a variable reduction analysis reveals that much information on the multireference character is provided by T₁, I_ND/I_tot, and the exchange-based diagnostic A₁₀₀[TPSS].

S66x8 noncovalent interactions revisited: new benchmark and performance of composite localized coupled-cluster methods

The S66x8 noncovalent interactions benchmark has been re-evaluated at the “sterling silver” level. Against this, a selection of computationally more economical alternatives has been assayed, ranging from localized CC to double hybrids and SAPT(DFT).

Accurate Quantum Chemical Prediction of Gas-Phase Anion Binding Affinities and Their Structure-Binding Relationships

This paper systematically examines the performance of contemporary wavefunction and density functional theory methods to identify robust and cost-efficient methods for predicting gas-phase anion binding energies. This includes the local coupled cluster LNO-CCSD(T) and DLPNO-CCSD(T), as well as double-hybrid DSD-PBEP86-D3(BJ) and various hybrid functionals M06-2X, B3LYP-D3(BJ), ωB97M-V, and ωB97X-V. The focus is on dual-hydrogen-bonding anion receptors that are commonly found in supramolecular chemistry and organocatalysis, namely, (thio)ureas, deltamides, (thio)squaramides, and croconamides as well as the yet-to-be-explored rhodizonamides. Of the methods examined, M06-2X emerged as the overall best performing method as the other functionals including DSD-PBEP86-D3(BJ) and the local coupled cluster DLPNO-CCSD(T) method displayed systematic errors that increase with the degree of carbonylation of the receptors. Hybrid ONIOM models that employed semiempirical methods (PM7, GFN1-xTB, and GFN2-xTB) and "threefold"-corrected small-basis set potentials (HF-3c, B97-3c, and PBEh-3c) were explored, and the best models resulted in 50- to 500-fold reduction in CPU time compared to W1-local. These calculations provide important insight into the structure-binding relationships where there is a direct correlation between Brønsted acidity and anion binding affinity, though the strength of the correlation also depends on other factors such as hydrogen-bonding geometry and the geometrical distortion that the receptor needs to undergo to bind the anion.

Efficient Ab Initio Estimation of Formation Enthalpies for Organic Compounds: Extension to Sulfur and Critical Evaluation of Experimental Data

The efficient protocol for the estimation of gas-phase enthalpies of formation developed previously for C, H, O, N, and F elements was extended to sulfur. The protocol is based on a local coupled cluster with single, double, and perturbative triple excitation [CCSD(T)] approximation and allows rapid evaluation of compounds with sizes computationally prohibitive to canonical CCSD(T) using quadruple zeta basis sets. As a part of model development, a comprehensive review and critical evaluation of experimental data were performed for 87 sulfur-containing organic and inorganic compounds. A compact model with only three empirical parameters for sulfur introduced to address the effects beyond frozen core CCSD(T) was developed. The model exhibits approximately 2 kJ·mol^-1 standard deviation over a set of experimental values for a diverse collection of sulfur-containing compounds. The complete basis set version of the model demonstrates a similar performance and requires only one empirical parameter. Multiple problems with the existing experimental data were identified and discussed. In addition, a lack of reliable data for certain important classes of sulfur compounds was found to impede the model generalization and confident performance assessment.

Methyl-Induced Polarization Destabilizes the Noncovalent Interactions of N-Methylated Lysines

Lysine methylation can modify noncovalent interactions by altering lysine's hydrophobicity as well as its electronic structure. Although the ramifications of the former are documented, the effects of the latter remain largely unknown. Understanding the electronic structure is important for determining how biological methylation modulates protein-protein binding, and the impact of artificial methylation experiments in which methylated lysines are used as spectroscopic probes and protein crystallization facilitators. The benchmarked first-principles calculations undertaken here reveal that methyl-induced polarization weakens the electrostatic attraction of amines with protein functional groups - salt bridges, hydrogen bonds and cation-π interactions weaken by as much as 10.3, 7.9 and 3.5 kT, respectively. Multipole analysis shows that weakened electrostatics is due to the altered inductive effects, which overcome increased attraction from methyl-enhanced polarizability and dispersion. Due to their fundamental nature, these effects are expected to be present in many cases. A survey of methylated lysines in protein structures reveals several cases in which methyl-induced polarization is the primary driver of altered noncovalent interactions; in these cases, destabilizations are found to be in the 0.6-4.7 kT range. The clearest case of where methyl-induced polarization plays a dominant role in regulating biological function is that of the PHD1-PHD2 domain, which recognizes lysine-methylated states on histones. These results broaden our understanding of how methylation modulates noncovalent interactions.

A Massively Parallel Implementation of the CCSD(T) Method Using the Resolution-of-the-Identity Approximation and a Hybrid Distributed/Shared Memory Parallelization Model

A parallel algorithm is described for the coupled-cluster singles and doubles method augmented with a perturbative correction for triple excitations [CCSD(T)] using the resolution-of-the-identity (RI) approximation for two-electron repulsion integrals (ERIs). The algorithm bypasses the storage of four-center ERIs by adopting an integral-direct strategy. The CCSD amplitude equations are given in a compact quasi-linear form by factorizing them in terms of amplitude-dressed three-center intermediates. A hybrid MPI/OpenMP parallelization scheme is employed, which uses the OpenMP-based shared memory model for intranode parallelization and the MPI-based distributed memory model for internode parallelization. Parallel efficiency has been optimized for all terms in the CCSD amplitude equations. Two different algorithms have been implemented for the rate-limiting terms in the CCSD amplitude equations that entail O(NO2NV4) and O(NO3NV3)-scaling computational costs, where N_O and N_V denote the number of correlated occupied and virtual orbitals, respectively. One of the algorithms assembles the four-center ERIs requiring N_V⁴ and N_O²N_V²-scaling memory costs in a distributed manner on a number of MPI ranks, while the other algorithm completely bypasses the assembling of quartic memory-scaling ERIs and thus largely reduces the memory demand. It is demonstrated that the former memory-expensive algorithm is faster on a few hundred cores, while the latter memory-economic algorithm shows a better strong scaling in the limit of a few thousand cores. The program is shown to exhibit a near-linear scaling, in particular for the compute-intensive triples correction step, on up to 8000 cores. The performance of the program is demonstrated via calculations involving molecules with 24-51 atoms and up to 1624 atomic basis functions. As the first application, the complete basis set (CBS) limit for the interaction energy of the π-stacked uracil dimer from the S66 data set has been investigated. This work reports the first calculation of the interaction energy at the CCSD(T)/aug-cc-pVQZ level without local orbital approximation. The CBS limit for the CCSD correlation contribution to the interaction energy was found to be -8.01 kcal/mol, which agrees very well with the value -7.99 kcal/mol reported by Schmitz, Hättig, and Tew [ Phys. Chem. Chem. Phys. 2014, 16, 22167-22178]. The CBS limit for the total interaction energy was estimated to be -9.64 kcal/mol.

Interactions between large molecules pose a puzzle for reference quantum mechanical methods

Quantum-mechanical methods are used for understanding molecular interactions throughout the natural sciences. Quantum diffusion Monte Carlo (DMC) and coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] are state-of-the-art trusted wavefunction methods that have been shown to yield accurate interaction energies for small organic molecules. These methods provide valuable reference information for widely-used semi-empirical and machine learning potentials, especially where experimental information is scarce. However, agreement for systems beyond small molecules is a crucial remaining milestone for cementing the benchmark accuracy of these methods. We show that CCSD(T) and DMC interaction energies are not consistent for a set of polarizable supramolecules. Whilst there is agreement for some of the complexes, in a few key systems disagreements of up to 8 kcal mol^-1 remain. These findings thus indicate that more caution is required when aiming at reproducible non-covalent interactions between extended molecules.

Accurate Reduced-Cost CCSD(T) Energies: Parallel Implementation, Benchmarks, and Large-Scale Applications

The accurate and systematically improvable frozen natural orbital (FNO) and natural auxiliary function (NAF) cost-reducing approaches are combined with our recent coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] implementations. Both of the closed- and open-shell FNO-CCSD(T) codes benefit from OpenMP parallelism, completely or partially integral-direct density-fitting algorithms, checkpointing, and hand-optimized, memory- and operation count effective implementations exploiting all permutational symmetries. The closed-shell CCSD(T) code requires negligible disk I/O and network bandwidth, is MPI/OpenMP parallel, and exhibits outstanding peak performance utilization of 50-70% up to hundreds of cores. Conservative FNO and NAF truncation thresholds benchmarked for challenging reaction, atomization, and ionization energies of both closed- and open-shell species are shown to maintain 1 kJ/mol accuracy against canonical CCSD(T) for systems of 31-43 atoms even with large basis sets. The cost reduction of up to an order of magnitude achieved extends the reach of FNO-CCSD(T) to systems of 50-75 atoms (up to 2124 atomic orbitals) with triple- and quadruple-ζ basis sets, which is unprecedented without local approximations. Consequently, a considerably larger portion of the chemical compound space can now be covered by the practically "gold standard" quality FNO-CCSD(T) method using affordable resources and about a week of wall time. Large-scale applications are presented for organocatalytic and transition-metal reactions as well as noncovalent interactions. Possible applications for benchmarking local CCSD(T) methods, as well as for the accuracy assessment or parametrization of less complete models, for example, density functional approximations or machine learning potentials, are also outlined.

Scalable Electron Correlation Methods. 8. Explicitly Correlated Open-Shell Coupled-Cluster with Pair Natural Orbitals PNO-RCCSD(T)-F12 and PNO-UCCSD(T)-F12

We present explicitly correlated open-shell pair natural orbital local coupled-cluster methods, PNO-RCCSD(T)-F12 and PNO-UCCSD(T)-F12. The methods are extensions of our previously reported PNO-R/UCCSD methods (J. Chem. Theory Comput., 2020, 16, 3135-3151, https://pubs.acs.org/doi/10.1021/acs.jctc.0c00192) with additions of explicit correlation and perturbative triples corrections. The explicit correlation treatment follows the spin-orbital CCSD-F12b theory using Ansatz 3*A, which is found to yield comparable or better basis set convergence than the more rigorous Ansatz 3C in computed ionization potentials and reaction energies using double- to quaduple-ζ basis sets. The perturbative triples correction is adapted from the spin-orbital (T) theory to use triples natural orbitals (TNOs). To address the coupling due to off-diagonal Fock matrix elements, the local triples amplitudes are iteratively solved using small domains of TNOs, and a semicanonical (T0) domain correction with larger domains is applied to reduce the domain errors. The performance of the methods is demonstrated through benchmark calculations on ionization potentials, radical stabilization energies, reaction energies of fragmentations and rearrangements in radical cations, and spin-state energy differences of iron complexes. For a few test sets where canonical calculations are feasible, PNO-RCCSD(T)-F12 results agree with the canonical ones to within 0.4 kcal mol^-1, and this maximum error is reduced to below 0.2 kcal mol^-1 when large local domains are used. For larger systems, results using different thresholds for the local approximations are compared to demonstrate that 1 kcal mol^-1 level of accuracy can be achieved using our default settings. For a couple of difficult cases, it is demonstrated that the errors from individual approximations are only a fraction of 1 kcal mol^-1, and the overall accuracy of the method does not rely on error compensations. In contrast to canonical calculations, the use of spin-orbitals does not lead to a significant increase of computational time and memory usage in the most expensive steps of PNO-R/UCCSD(T)-F12 calculations. The only exception is the iterative solution of the (T) amplitudes, which can be avoided without significant errors by using a perturbative treatment of the off-diagonal coupling, known as (T1) approximation. For most systems, even the semicanonical approximation (T0) leads only to small errors in relative energies. Our program is well parallelized and capable of computing accurate correlation energies for molecules with 100-200 atoms using augmented triple-ζ basis sets in less than a day of elapsed time on a small computer cluster.

Canonical and explicitly-correlated coupled cluster correlation energies of sub-kJ mol-1 accuracy via cost-effective hybrid-post-CBS extrapolation

Cost-effectiveness and accuracy are two basic pillars in electronic structure calculations. While cost-effectiveness enhances applicability, high accuracy is sustained when employing advanced computational tools. With the gold standard method of ab initio quantum chemistry at the focal point, canonical CCSD(T) and modern explicitly correlated CCSD(T)-F12 calculations are employed hand in hand to develop accurate hybrid post-CBS extrapolation schemes, which are validated using popular training sets involving a total of 130 molecules. By using raw valence-only calculations at CCSD(T)/VDZ and CCSD(T)/VQZ-F12 levels of theory, the novel scheme leads to the prediction of absolute energies that differ on average (-0.170 ± 0.224) kcal mol-1 from the highest affordable CCSD(T)-F12b/V(Q,5)Z-F12 extrapolations, but only (-0.048 ± 0.228) kcal mol-1 from the post-CBS extrapolated values based on CBS(D,T), CBS(D,Q) and CBS(T,Q) energies. From the cost-effectiveness standpoint, the approach is a kind of pseudo one-point extrapolation scheme since its cost is basically that of the highest-rung raw energy where it is based. Variants that imply no additional cost are also discussed, emerging h-pCBS(dt,dq)ab as the most effective. The approach can also be used with PNO-based local correlation methods that gained popularity due to allowing coupled-cluster calculations even for large molecules at reduced computational cost, namely local PNO-CCSD(T) and PNO-CCSD(T)-F12b. To gauge the approach performance, both the hydrogen molecule and the O-C2H5 torsion path of ethyl-methyl-ether, an extra molecule here considered with presupposed existence in astrophysical objects, are also studied. Additionally, the nonbonding interactions in the A24 test set are revisited per se. The results show that the title approach may be useful in high-accuracy quantum chemistry, with further improvements requiring the inclusion of contributions beyond the theory here employed such as the ones due to relativistic and nonadiabatic effects.

Transferable interactions of Li+ and Mg2+ ions in polarizable models

Therapeutic implications of Li⁺, in many cases, stem from its ability to inhibit certain Mg²⁺-dependent enzymes, where it interacts with or substitutes for Mg²⁺. The underlying details of its action are, however, unknown. Molecular simulations can provide insights, but their reliability depends on how well they describe relative interactions of Li⁺ and Mg²⁺ with water and other biochemical groups. Here, we explore, benchmark, and recommend improvements to two simulation approaches: the one that employs an all-atom polarizable molecular mechanics (MM) model and the other that uses a hybrid quantum and MM implementation of the quasi-chemical theory (QCT). The strength of the former is that it describes thermal motions explicitly and that of the latter is that it derives local contributions from electron densities. Reference data are taken from the experiment, and also obtained systematically from CCSD(T) theory, followed by a benchmarked vdW-inclusive density functional theory. We find that the QCT model predicts relative hydration energies and structures in agreement with the experiment and without the need for additional parameterization. This implies that accurate descriptions of local interactions are essential. Consistent with this observation, recalibration of local interactions in the MM model, which reduces errors from 10.0 kcal/mol to 1.4 kcal/mol, also fixes aqueous phase properties. Finally, we show that ion-ligand transferability errors in the MM model can be reduced significantly from 10.3 kcal/mol to 1.2 kcal/mol by correcting the ligand's polarization term and by introducing Lennard-Jones cross-terms. In general, this work sets up systematic approaches to evaluate and improve molecular models of ions binding to proteins.

Improved description of ligand polarization enhances transferability of ion-ligand interactions

The reliability of molecular mechanics (MM) simulations in describing biomolecular ion-driven processes depends on their ability to accurately model interactions of ions simultaneously with water and other biochemical groups. In these models, ion descriptors are calibrated against reference data on ion-water interactions, and it is then assumed that these descriptors will also satisfactorily describe interactions of ions with other biochemical ligands. The comparison against the experiment and high-level quantum mechanical data show that this transferability assumption can break down severely. One approach to improve transferability is to assign cross terms or separate sets of non-bonded descriptors for every distinct pair of ion type and its coordinating ligand. Here, we propose an alternative solution that targets an error-source directly and corrects misrepresented physics. In standard model development, ligand descriptors are never calibrated or benchmarked in the high electric fields present near ions. We demonstrate for a representative MM model that when the polarization descriptors of its ligands are improved to respond to both low and high fields, ligand interactions with ions also improve, and transferability errors reduce substantially. In our case, the overall transferability error reduces from 3.3 kcal/mol to 1.8 kcal/mol. These improvements are observed without compromising on the accuracy of low-field interactions of ligands in gas and condensed phases. Reference data for calibration and performance evaluation are taken from the experiment and also obtained systematically from "gold-standard" CCSD(T) in the complete basis set limit, followed by benchmarked vdW-inclusive density functional theory.

Double hybrid DFT calculations with Slater type orbitals

On a comprehensive database with 1,644 datapoints, covering several aspects of main-group as well as of transition metal chemistry, we assess the performance of 60 density functional approximations (DFA), among them 36 double hybrids (DH). All calculations are performed using a Slater type orbital (STO) basis set of triple-ζ (TZ) quality and the highly efficient pair atomic resolution of the identity approach for the exchange- and Coulomb-term of the KS matrix (PARI-K and PARI-J, respectively) and for the evaluation of the MP2 energy correction (PARI-MP2). Employing the quadratic scaling SOS-AO-PARI-MP2 algorithm, DHs based on the spin-opposite-scaled (SOS) MP2 approximation are benchmarked against a database of large molecules. We evaluate the accuracy of STO/PARI calculations for B3LYP as well as for the DH B2GP-PLYP and show that the combined basis set and PARI-error is comparable to the one obtained using the well-known def2-TZVPP Gaussian-type basis set in conjunction with global density fitting. While quadruple-ζ (QZ) calculations are currently not feasible for PARI-MP2 due to numerical issues, we show that, on the TZ level, Jacob's ladder for classifying DFAs is reproduced. However, while the best DHs are more accurate than the best hybrids, the improvements are less pronounced than the ones commonly found on the QZ level. For conformers of organic molecules and noncovalent interactions where very high accuracy is required for qualitatively correct results, DHs provide only small improvements over hybrids, while they still excel in thermochemistry, kinetics, transition metal chemistry and the description of strained organic systems.

A Quadratic Pair Atomic Resolution of the Identity Based SOS-AO-MP2 Algorithm Using Slater Type Orbitals

We report a production level implementation of pair atomic resolution of the identity (PARI) based second-order Møller-Plesset perturbation theory (MP2) in the Slater type orbital (STO) based Amsterdam Density Functional (ADF) code. As demonstrated by systematic benchmarks, dimerization and isomerization energies obtained with our code using STO basis sets of triple-ζ-quality show mean absolute deviations from Gaussian type orbital, canonical, basis set limit extrapolated, global density fitting (DF)-MP2 results of less than 1 kcal/mol. Furthermore, we introduce a quadratic scaling atomic orbital based spin-opposite-scaled (SOS)-MP2 approach with a very small prefactor. Due to a worst-case scaling of [Formula: see text], our implementation is very fast already for small systems and shows an exceptionally early crossover to canonical SOS-PARI-MP2. We report computational wall time results for linear as well as for realistic three-dimensional molecules and show that triple-ζ quality calculations on molecules of several hundreds of atoms are only a matter of a few hours on a single compute node, the bottleneck of the computations being the SCF rather than the post-SCF energy correction.

Heat capacity and decomposition of rimantadine hydrochloride

Heat capacities of the antiviral drug rimantadine hydrochloride in the crystalline state were measured by adiabatic calorimetry and differential scanning calorimetry in the temperature range from (7 to 453) K. A broad low-enthalpy solid-state phase anomaly was detected between (170 and 250) K. Thermodynamic functions for crystalline rimantadine hydrochloride were derived. Decomposition of the studied compound was probed by the Knudsen effusion method and thermogravimetry with the support of quantum chemical calculations. The enthalpy of decomposition of rimantadine hydrochloride into the corresponding amine and hydrogen chloride was estimated from those data. The thermodynamic functions of the corresponding amine in the ideal gaseous state, including enthalpy of formation, were obtained using statistical thermodynamics with the necessary molecular parameters computed using quantum chemical methods. The enthalpy of formation of crystalline rimantadine hydrochloride was estimated.

Non-covalent Interactions and Charge Transfer between Propene and Neutral Yttrium-Doped and Pure Gold Clusters

The dopant and size-dependent propene adsorption on neutral gold (Aun ) and yttrium-doped gold (Aun-1 Y) clusters in the n=5-15 size range are investigated, combining mass spectrometry and gas phase reactions in a low-pressure collision cell and density functional theory calculations. The adsorption energies, extracted from the experimental data using an RRKM analysis, show a similar size dependence as the quantum chemical results and are in the range of ≈0.6-1.2 eV. Yttrium doping significantly alters the propene adsorption energies for n=5, 12 and 13. Chemical bonding and energy decomposition analysis showed that there is no covalent bond between the cluster and propene, and that charge transfer and other non-covalent interactions are dominant. The natural charges, Wiberg bond indices, and the importance of charge transfer all support an electron donation/back-donation mechanism for the adsorption. Yttrium plays a significant role not only in the propene binding energy, but also in the chemical bonding in the cluster-propene adduct. Propene preferentially binds to yttrium in small clusters (n<10), and to a gold atom at larger sizes. Besides charge transfer, relaxation also plays an important role, illustrating the non-local effect of the yttrium dopant. It is shown that the frontier molecular orbitals of the clusters determine the chemical bonding, in line with the molecular-like electronic structure of metal clusters.