Accurate Noncovalent Interaction Energies Using Truncated Basis Sets Based on Frozen Natural Orbitals

Frozen Natural Orbitals for the State-Averaged Driven Similarity Renormalization Group

We present a reduced-cost implementation of the state-averaged driven similarity renormalization group (SA-DSRG) based on the frozen natural orbital (FNO) approach. The natural orbitals (NOs) are obtained by diagonalizing the one-body reduced density matrix from SA-DSRG second-order perturbation theory (SA-DSRG-PT2). We consider three criteria to truncate the virtual NOs for the subsequent electron correlation treatment beyond SA-DSRG-PT2. An additive second-order correction is applied to the SA-DSRG Hamiltonian to reintroduce correlation effects from the discarded orbitals. The FNO SA-DSRG method is benchmarked on 35 small organic molecules in the QUEST database. When keeping 98-99% of the cumulative occupation numbers, the mean absolute error in the vertical transition energies due to FNO is less than 0.01 eV. Using the same FNO threshold, we observe a speedup of 9 times compared to the conventional SA-DSRG implementation for nickel carbonyl with a quadruple-ζ basis set. The FNO approach enables nonperturbative SA-DSRG computations on chloroiron corrole [FeCl(C19H11N4)] with more than 1000 basis functions, surpassing the current limit of a conventional implementation.

Toward Accurate Post-Born-Oppenheimer Molecular Simulations on Quantum Computers: An Adaptive Variational Eigensolver with Nuclear-Electronic Frozen Natural Orbitals

Nuclear quantum effects such as zero-point energy and hydrogen tunneling play a central role in many biological and chemical processes. The nuclear-electronic orbital (NEO) approach captures these effects by treating selected nuclei quantum mechanically on the same footing as electrons. On classical computers, the resources required for an exact solution of NEO-based models grow exponentially with system size. By contrast, quantum computers offer a means of solving this problem with polynomial scaling. However, due to the limitations of current quantum devices, NEO simulations are confined to the smallest systems described by minimal basis sets, whereas realistic simulations beyond the Born-Oppenheimer approximation require more sophisticated basis sets. For this purpose, we herein extend a hardware-efficient ADAPT-VQE method to the NEO framework in the frozen natural orbital (FNO) basis. We demonstrate on H2 and D2 molecules that the NEO-FNO-ADAPT-VQE method reduces the CNOT count by several orders of magnitude relative to the NEO unitary coupled cluster method with singles and doubles while maintaining the desired accuracy. This extreme reduction in the CNOT gate count is sufficient to permit practical computations employing the NEO method─an important step toward accurate simulations involving nonclassical nuclei and non-Born-Oppenheimer effects on near-term quantum devices. We further show that the method can capture isotope effects, and we demonstrate that inclusion of correlation energy systematically improves the prediction of difference in the zero-point energy (ΔZPE) between isotopes.

Natural virtual orbitals for the GW method in the random-phase approximation and beyond

The increasingly popular GW method is becoming a convenient tool to determine vertical ionization energies in molecular systems. However, depending on the formalism used and the range of orbitals investigated, it may be hampered by a steep computational scaling. To alleviate this issue, correlated natural virtual orbitals (NVOs) based on second-order Møller-Plesset (MP2) and direct MP2 correlation energies are implemented, and the resulting correlated NVOs are tested on GW quasiparticle energies. Test cases include the popular GW variants G₀W₀ and evGW₀ as well as more elaborate vertex corrections. We find that for increasingly larger molecular systems and basis sets, NVOs considerably improve efficiency. Furthermore, we test the performance of the truncated (frozen) NVO ansatz on the GW100 test set. For the latter, it is demonstrated that, using a carefully chosen truncation threshold, NVOs lead to a negligible loss in accuracy while providing speedups of one order of magnitude. Furthermore, we compare the resulting quasiparticle energies to very accurate vertical ionization energies obtained from coupled-cluster theory with singles, doubles, and noniterative triples [CCSD(T)], confirming that the loss in accuracy introduced by truncating the NVOs is negligible compared to the methodical errors in the GW approximation. It is also demonstrated that the choice of basis set impacts results far more than using a suitably truncated NVO space. Therefore, at the same computational expense, more accurate results can be obtained using NVOs. Finally, we provide improved reference CCSD(T) values for the GW100 test set, which have been obtained using the def2-QZVPP basis set.

Electronic structure theory on modeling short-range noncovalent interactions between amino acids

While short-range noncovalent interactions (NCIs) are proving to be of importance in many chemical and biological systems, these atypical bindings happen within the so-called van der Waals envelope and pose an enormous challenge for current computational methods. We introduce SNCIAA, a database of 723 benchmark interaction energies of short-range noncovalent interactions between neutral/charged amino acids originated from protein x-ray crystal structures at the "gold standard" coupled-cluster with singles, doubles, and perturbative triples/complete basis set [CCSD(T)/CBS] level of theory with a mean absolute binding uncertainty less than 0.1 kcal/mol. Subsequently, a systematic assessment of commonly used computational methods, such as the second-order Møller-Plesset theory (MP2), density functional theory (DFT), symmetry-adapted perturbation theory (SAPT), composite electronic-structure methods, semiempirical approaches, and the physical-based potentials with machine learning (IPML) on SNCIAA is carried out. It is shown that the inclusion of dispersion corrections is essential even though these dimers are dominated by electrostatics, such as hydrogen bondings and salt bridges. Overall, MP2, ωB97M-V, and B3LYP+D4 turned out to be the most reliable methods for the description of short-range NCIs even in strongly attractive/repulsive complexes. SAPT is also recommended in describing short-range NCIs only if the δMP2 correction has been included. The good performance of IPML for dimers at close-equilibrium and long-range conditions is not transferable to the short-range. We expect that SNCIAA will assist the development/improvement/validation of computational methods, such as DFT, force-fields, and ML models, in describing NCIs across entire potential energy surfaces (short-, intermediate-, and long-range NCIs) on the same footing.

Effects of Microhydration on the Mechanisms of Hydrolysis and Cl- Substitution in Reactions of N2 O5 and Seawater

The reaction of N₂ O₅ at atmospheric interfaces has recently received considerable attention due to its importance in atmospheric chemistry. N₂ O₅ reacts preferentially with Cl^- to form ClNO₂ /NO₃ ^- (Cl^- substitution), but can also react with H₂ O to form 2HNO₃ (hydrolysis). In this paper, we explore these competing reactions in a theoretical study of the clusters N₂ O₅ /Cl^- /nH₂ O (n=2-5), resulting in the identification of three reaction motifs. First, we uncovered an S_N 2-type Cl^- substitution reaction of N₂ O₅ that occurs very quickly due to low barriers to reaction. Second, we found a low-lying pathway to hydrolysis via a ClNO₂ intermediate (two-step hydrolysis). Finally, we found a direct hydrolysis pathway where H₂ O attacks N₂ O₅ (one-step hydrolysis). We find that Cl^- substitution is the fastest reaction in every cluster. Between one-step and two-step hydrolysis, we find that one-step hydrolysis barriers are lower, making two-step hydrolysis (via ClNO₂ intermediate) likely only when concentrations of Cl^- are high.

Basis Set Limit CCSD(T) Energies for Extended Molecules via a Reduced-Cost Explicitly Correlated Approach

Several approximations are introduced and tested to reduce the computational expenses of the explicitly correlated coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method for both closed and open-shell species. First, the well-established frozen natural orbital (FNO) technique is adapted to explicitly correlated CC approaches. Second, our natural auxiliary function (NAF) scheme is employed to reduce the size of the auxiliary basis required for the density fitting approximation regularly used in explicitly correlated calculations. Third, a new approach, termed the natural auxiliary basis (NAB) approximation, is proposed to decrease the size of the auxiliary basis needed for the expansion of the explicitly correlated geminals. The performance of the above approximations and that of the combined FNO-NAF-NAB approach are tested for atomization and reaction energies. Our results show that overall speedups of 7-, 5-, and 3-times can be achieved with double-, triple-, and quadruple-ζ basis sets, respectively, without any loss in accuracy. The new method can provide, e.g., reaction energies and barrier heights well within chemical accuracy for molecules with more than 40 atoms within a few days using a few dozen processor cores, and calculations with 50+ atoms are still feasible. These routinely affordable computations considerably extend the reach of explicitly correlated CCSD(T).

Linear-Scaling Systematic Molecular Fragmentation Approach for Perturbation Theory and Coupled-Cluster Methods

The coupled-cluster (CC) singles and doubles with perturbative triples [CCSD(T)] method is frequently referred to as the “gold standard” of modern computational chemistry. However, the high computational cost of CCSD(T) [O(N⁷)], where N is the number of basis functions, limits its applications to small-sized chemical systems. To address this problem, efficient implementations of linear-scaling coupled-cluster methods, which employ the systematic molecular fragmentation (SMF) approach, are reported. In this study, we aim to do the following: (1) To achieve exact linear scaling and to obtain a pure ab initio approach, we revise the handling of nonbonded interactions in the SMF approach, denoted by LSSMF. (2) A new fragmentation algorithm, which yields smaller-sized fragments, that better fits high-level CC methods is introduced. (3) A modified nonbonded fragmentation scheme is proposed to enhance the existent algorithm. Performances of the LSSMF-CC approaches, such as LSSMF-CCSD(T), are compared with their canonical versions for a set of alkane molecules, C_nH_2n+2 (n = 6–10), which includes 142 molecules. Our results demonstrate that the LSSMF approach introduces negligible errors compared with the canonical methods; mean absolute errors (MAEs) are between 0.20 and 0.59 kcal mol^–1 for LSSMF(3,1)-CCSD(T). For a larger alkanes set (L12), C_nH_2n+2 (n = 50–70), the performance of LSSMF for the second-order perturbation theory (MP2) is investigated. For the L12 set, various bonded and nonbonded levels are considered. Our results demonstrate that the combination of bonded level 6 with nonbonded level 2, LSSMF(6,2), provides very accurate results for the MP2 method with a MAE value of 0.32 kcal mol^–1. The LSSMF(6,2) approach yields more than a 26-fold reduction in errors compared with LSSMF(3,1). Hence, we obtain substantial improvements over the original SMF approach. To illustrate the efficiency and applicability of the LSSMF-CCSD(T) approach, we consider an alkane molecule with 10,004 atoms. For this molecule, the LSSMF(3,1)-CCSD(T)/cc-pVTZ energy computation, on a Linux cluster with 100 nodes, 4 cores, and 5 GB of memory provided to each node, is performed just in ∼24 h. As a second test, we consider a biomolecular complex (PDB code: 1GLA), which includes 10,488 atoms, to assess the efficiency of the LSSMF approach. The LSSMF(3,1)-FNO–CCSD(T)/cc-pVTZ energy computation is completed in ∼7 days for the biomolecular complex. Hence, our results demonstrate that the LSSMF-CC approaches are very efficient. Overall, we conclude the following: (1) The LSSMF(m, n)-CCSD(T) methods can be reliably used for large-scale chemical systems, where the canonical methods are not computationally affordable. (2) The accuracy of bonded level 3 is not satisfactory for large chemical systems. (3) For high-accuracy studies, bonded level 5 (or higher) and nonbonded level 2 should be employed.

Efficient implementation of molecular CCSD gradients with Cholesky-decomposed electron repulsion integrals

We present an efficient implementation of ground and excited state coupled cluster singles and doubles (CCSD) gradients based on Cholesky-decomposed electron repulsion integrals. Cholesky decomposition and density fitting are both inner projection methods, and, thus, similar implementation schemes can be applied for both methods. One well-known advantage of inner projection methods, which we exploit in our implementation, is that one can avoid storing large V3 O and V4 arrays by instead considering three-index intermediates. Furthermore, our implementation does not require the formation and storage of Cholesky vector derivatives. The new implementation is shown to perform well, with less than 10% of the time spent calculating the gradients in geometry optimizations. Furthermore, the computational time per optimization cycle is significantly lower compared to other implementations based on an inner projection method. We showcase the capabilities of the implementation by optimizing the geometry of the retinal molecule (C20H28O) at the CCSD/aug-cc-pVDZ level of theory.

Assessing the persistence of chalcogen bonds in solution with neural network potentials

Non-covalent bonding patterns are commonly harvested as a design principle in the field of catalysis, supramolecular chemistry and functional materials to name a few. Yet, their computational description generally neglects finite temperature and environment effects, which promote competing interactions and alter their static gas-phase properties. Recently, neural network potentials (NNPs) trained on Density Functional Theory (DFT) data have become increasingly popular to simulate molecular phenomena in condensed phase with an accuracy comparable to ab initio methods. To date, most applications have centered on solid-state materials or fairly simple molecules made of a limited number of elements. Herein, we focus on the persistence and strength of chalcogen bonds involving a benzotelluradiazole in condensed phase. While the tellurium-containing heteroaromatic molecules are known to exhibit pronounced interactions with anions and lone pairs of different atoms, the relevance of competing intermolecular interactions, notably with the solvent, is complicated to monitor experimentally but also challenging to model at an accurate electronic structure level. Here, we train direct and baselined NNPs to reproduce hybrid DFT energies and forces in order to identify what are the most prevalent non-covalent interactions occurring in a solute-Cl$^-$-THF mixture. The simulations in explicit solvent highlight competition with chalcogen bonds formed with the solvent and the short-range directionality of the interaction with direct consequences for the molecular properties in the solution. The comparison with other potentials (e.g., AMOEBA, direct NNP and continuum solvent model) also demonstrates that baselined NNPs offer a reliable picture of the non-covalent interaction interplay occurring in solution.

Short-Range Imbalances in the AMBER Lennard-Jones Potential for (Deoxy)Ribose···Nucleobase Lone-Pair···π Contacts in Nucleic Acids

The lone-pair···π (lp···π) (deoxy)ribose···nucleobase stacking is a recurring interaction in Z-DNA and RNAs that is characterized by sub-van der Waals lp···π contacts (<3.0 Å). It is a part of the structural signature of CpG Z-step motifs in Z-DNA and r(UNCG) tetraloops that are known to behave poorly in molecular dynamics (MD) simulations. Although the exact origin of the MD simulation issues remains unclear, a significant part of the problem might be due to an imbalanced description of nonbonded interactions, including the characteristic lp···π stacking. To gain insights into the links between lp···π stacking and MD, we present an in-depth comparison between accurate large-basis-set double-hybrid Kohn-Sham density functional theory calculations DSD-BLYP-D3/ma-def2-QZVPP (DHDF-D3) and data obtained with the nonbonded potential of the AMBER force field (AFF) for NpN Z-steps (N = G, A, C, and U). Among other differences, we found that the AFF overestimates the DHDF-D3 lp···π distances by ∼0.1-0.2 Å, while the deviation between the DHDF-D3 and AFF descriptions sharply increases in the short-range region of the interaction. Based on atom-in-molecule polarizabilities and symmetry-adapted perturbation theory analysis, we inferred that the DHDF-D3 versus AFF differences partly originate in identical nucleobase carbon atom Lennard-Jones (LJ) parameters despite the presence/absence of connected electron-withdrawing groups that lead to different effective volumes or vdW radii. Thus, to precisely model the very short CpG lp···π contact distances, we recommend revision of the nucleobase atom LJ parameters. Additionally, we suggest that the large discrepancy between DHDF-D3 and AFF short-range repulsive part of the interaction energy potential may significantly contribute to the poor performances of MD simulations of nucleic acid systems containing Z-steps. Understanding where, and if possible why, the point-charge-type effective potentials reach their limits is vital for developing next-generation FFs and for addressing specific issues in contemporary MD simulations.

Coupled cluster benchmarks of large noncovalent complexes: The L7 dataset as well as DNA-ellipticine and buckycatcher-fullerene

In this work, benchmark binding energies for dispersion-bound complexes in the L7 dataset, the DNA-ellipticine intercalation complex, and the buckycatcher-C₆₀ complex with 120 heavy atoms using a focal-point method based on the canonical form of second-order Møller-Plesset theory (MP2) and the domain based local pair natural orbital scheme for the coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] extrapolated to the complete basis set (CBS) limit are reported. This work allows for increased confidence given the agreement with respect to values recently obtained using the local natural orbital CCSD(T) for L7 and the canonical CCSD(T)/CBS result for the coronene dimer (C2C2PD). Therefore, these results can be considered pushing the CCSD(T)/CBS binding benchmark to the hundred-atom scale. The disagreements between the two state-of-the-art methods, CCSD(T) and fixed-node diffusion Monte Carlo, are substantial with at least 2.0 (∼10%), 1.9 (∼5%), and 10.3 kcal/mol (∼25%) differences for C2C2PD in L7, DNA-ellipticine, and buckycatcher-C₆₀, respectively. Such sizable discrepancy above "chemical accuracy" for large noncovalent complexes indicates how challenging it is to obtain benchmark binding interactions for systems beyond small molecules, although the three up-to-date density functionals, PBE0+D4, ωB97M-V, and B97M-V, agree better with CCSD(T) for these large systems. In addition to reporting these values, different basis sets and various CBS extrapolation parameters for Hartree-Fock and MP2 correlation energies were tested for the first time in large noncovalent complexes with the goal of providing some indications toward optimal cost effective routes to approach the CBS limit without substantial loss in quality.

Highly Accurate Many-Body Potentials for Simulations of N2O5 in Water: Benchmarks, Development, and Validation

Dinitrogen pentoxide (N₂O₅) is an important intermediate in the atmospheric chemistry of nitrogen oxides. Although there has been much research, the processes that govern the physical interactions between N₂O₅ and water are still not fully understood at a molecular level. Gaining a quantitative insight from computer simulations requires going beyond the accuracy of classical force fields while accessing length scales and time scales that are out of reach for high-level quantum-chemical approaches. To this end, we present the development of MB-nrg many-body potential energy functions for nonreactive simulations of N₂O₅ in water. This MB-nrg model is based on electronic structure calculations at the coupled cluster level of theory and is compatible with the successful MB-pol model for water. It provides a physically correct description of long-range many-body interactions in combination with an explicit representation of up to three-body short-range interactions in terms of multidimensional permutationally invariant polynomials. In order to further investigate the importance of the underlying interactions in the model, a TTM-nrg model was also devised. TTM-nrg is a more simplistic representation that contains only two-body short-range interactions represented through Born-Mayer functions. In this work, an active learning approach was employed to efficiently build representative training sets of monomer, dimer, and trimer structures, and benchmarks are presented to determine the accuracy of our new models in comparison to a range of density functional theory methods. By assessing the binding curves, distortion energies of N₂O₅, and interaction energies in clusters of N₂O₅ and water, we evaluate the importance of two-body and three-body short-range potentials. The results demonstrate that our MB-nrg model has high accuracy with respect to the coupled cluster reference, outperforms current density functional theory models, and thus enables highly accurate simulations of N₂O₅ in aqueous environments.

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.

Reducing Qubit Requirements while Maintaining Numerical Precision for the Variational Quantum Eigensolver: A Basis-Set-Free Approach

We present a basis-set-free approach to the variational quantum eigensolver using an adaptive representation of the spatial part of molecular wave functions. Our approach directly determines system-specific representations of qubit Hamiltonians while fully omitting globally defined basis sets. In this work, we use directly determined pair-natural orbitals on the level of second-order perturbation theory. This results in compact qubit Hamiltonians with high numerical accuracy. We demonstrate initial applications with compact Hamiltonians on up to 22 qubits where conventional representation would for the same systems require 40-100 or more qubits. We further demonstrate reductions in the quantum circuits through the structure of the pair-natural orbitals.

Multilevel CC2 and CCSD in Reduced Orbital Spaces: Electronic Excitations in Large Molecular Systems

We present efficient implementations of the multilevel CC2 (MLCC2) and multilevel CCSD (MLCCSD) models. As the system size increases, MLCC2 and MLCCSD exhibit the scaling of the lower-level coupled cluster model. To treat large systems, we combine MLCC2 and MLCCSD with a reduced-space approach in which the multilevel coupled cluster calculation is performed in a significantly truncated molecular orbital basis. The truncation scheme is based on the selection of an active region of the molecular system and the subsequent construction of localized Hartree-Fock orbitals. These orbitals are used in the multilevel coupled cluster calculation. The electron repulsion integrals are Cholesky decomposed using a screening protocol that guarantees accuracy in the truncated molecular orbital basis and reduces computational cost. The Cholesky factors are constructed directly in the truncated basis, ensuring low storage requirements. Systems for which Hartree-Fock is too expensive can be treated by using a multilevel Hartree-Fock reference. With the reduced-space approach, we can handle systems with more than a thousand atoms. This is demonstrated for paranitroaniline in aqueous solution.

Equation-of-Motion MLCCSD and CCSD-in-HF Oscillator Strengths and Their Application to Core Excitations

We present an implementation of equation-of-motion oscillator strengths for the multilevel CCSD (MLCCSD) model where CCS is used as the lower level method (CCS/CCSD). In this model, the double excitations of the cluster operator are restricted to an active orbital space, whereas the single excitations are unrestricted. Calculated nitrogen K-edge spectra of adenosine, adenosine triphosphate (ATP), and an ATP-water system are used to demonstrate the performance of the model. Projected atomic orbitals (PAOs) are used to partition the virtual space into active and inactive orbital sets. Cholesky decomposition of the Hartree-Fock density is used to partition the occupied orbitals. This Cholesky-PAO partitioning is cheap, scaling as O(N3), and is suitable for the calculation of core excitations, which are localized in character. By restricting the single excitations of the cluster operator to the active space, as well as the double excitations, the CCSD-in-HF model is obtained. A comparison of the two models-MLCCSD and CCSD-in-HF-is presented for the core excitation spectra of the adenosine and ATP systems.

Psi4 1.4: Open-source software for high-throughput quantum chemistry

PSI4 is a free and open-source ab initio electronic structure program providing implementations of Hartree-Fock, density functional theory, many-body perturbation theory, configuration interaction, density cumulant theory, symmetry-adapted perturbation theory, and coupled-cluster theory. Most of the methods are quite efficient, thanks to density fitting and multi-core parallelism. The program is a hybrid of C++ and Python, and calculations may be run with very simple text files or using the Python API, facilitating post-processing and complex workflows; method developers also have access to most of PSI4's core functionalities via Python. Job specification may be passed using The Molecular Sciences Software Institute (MolSSI) QCSCHEMA data format, facilitating interoperability. A rewrite of our top-level computation driver, and concomitant adoption of the MolSSI QCARCHIVE INFRASTRUCTURE project, makes the latest version of PSI4 well suited to distributed computation of large numbers of independent tasks. The project has fostered the development of independent software components that may be reused in other quantum chemistry programs.

Probing the Partial Activation of Water by Open-Shell Interactions, Cl(H2O)1-4

The partial chemical activation of water by reactive radicals was examined computationally for small clusters of chlorine and water, Cl^•(H₂O)_n=1-4. Using an automated isomer-search procedure, dozens of unique, stable structures were computed. Among the resulting structural classes were intact, hydrated-chlorine isomers, as well as hydrogen-abstracted (HCl)(OH)(H₂O)_n-1 configurations. The latter showed increased stability as the degree of hydration increased, until n = 4, where a new class of structures was discovered with a chloride ion bound to an oxidized water network. The electronic structure of these three structural classes was investigated, and spectral signatures of this hydration-based evolution were connected to these electronic properties. An ancillary outcome of this detailed computational analysis, including coupled-cluster benchmarks, was the calibration of cost-effective quantum chemistry methods for future studies of these radical-water complexes.

Revisiting the Potential Energy Surface of the Stacked Cytosine Dimer: FNO-CCSD(T) Interaction Energies, SAPT Decompositions, and Benchmarking

Nucleobase stacking interactions are crucial for the stability of nucleic acids. This study investigates base stacking energies of the cytosine homodimer in different configurations, including intermolecular separation plots, detailed twist dependence, and displaced structures. Highly accurate ab initio quantum chemical single point energies using an energy function based on MP2 complete basis set extrapolation ([6 → 7]ZaPa-NR) and a CCSD(T)/cc-pVTZ-F12 high-level correction are presented as new reference data, providing the most accurate stacking energies of nucleobase dimers currently available. Accurate SAPT2+(3)δMP2 energy decomposition is used to obtain detailed insights into the nature of base stacking interactions at varying vertical distances and twist values. The ab initio symmetry adapted perturbation theory (SAPT) energy decomposition suggests that the base stacking originates from an intricate interplay between dispersion attraction, short-range exchange-repulsion, and Coulomb interaction. The interpretation of the SAPT data is a complex issue as key energy terms vary substantially in the region of optimal (low energy) base stacking geometries. Thus, attempts to highlight one leading stabilizing SAPT base stacking term may be misleading and the outcome strongly depends on the used geometries within the range of geometries sampled in nucleic acids upon thermal fluctuations. Modern dispersion-corrected density functional theory (among them DSD-BLYP-D3, ωB97M-V, and ωB97M-D3BJ) is benchmarked and often reaches up to spectroscopic accuracy (below 1 kJ/mol). The classical AMBER force field is benchmarked with multiple different sets of point-charges (e.g. HF, DFT, and MP2-based) and is found to produce reasonable agreement with the benchmark data.

Accuracy and Resource Estimations for Quantum Chemistry on a Near-Term Quantum Computer

One of the most important application areas of molecular quantum chemistry is the study and prediction of chemical reactivity. Large-scale, fully error-tolerant quantum computers could provide exact or near-exact solutions to the underlying electronic structure problem with exponentially less effort than a classical computer thus enabling highly accurate predictions for comparably large molecular systems. In the nearer future, however, only "noisy" devices with a limited number of qubits that are subject to decoherence will be available. For such near-term quantum computers the hybrid quantum-classical variational quantum eigensolver algorithm in combination with the unitary coupled-cluster ansatz (UCCSD-VQE) [ Peruzzo et al. Nat. Commun. 2014 , 5 , 4213 and McClean et al. New J. Phys. 2016 , 18 , 023023 ] has become an intensively discussed approach that could provide accurate results before the dawn of error-tolerant quantum computing. In this work we present an implementation of UCCSD-VQE that allows for the first time to treat both open- and closed-shell molecules. We study the accuracy of the obtained energies for nine small molecular systems as well as for four exemplary chemical reactions by comparing to well-established electronic structure methods like (nonunitary) coupled-cluster and density functional theory. Finally, we roughly estimate the required quantum hardware resources to obtain "useful" results for practical purposes.

Psi4 1.1: An Open-Source Electronic Structure Program Emphasizing Automation, Advanced Libraries, and Interoperability

Psi4 is an ab initio electronic structure program providing methods such as Hartree-Fock, density functional theory, configuration interaction, and coupled-cluster theory. The 1.1 release represents a major update meant to automate complex tasks, such as geometry optimization using complete-basis-set extrapolation or focal-point methods. Conversion of the top-level code to a Python module means that Psi4 can now be used in complex workflows alongside other Python tools. Several new features have been added with the aid of libraries providing easy access to techniques such as density fitting, Cholesky decomposition, and Laplace denominators. The build system has been completely rewritten to simplify interoperability with independent, reusable software components for quantum chemistry. Finally, a wide range of new theoretical methods and analyses have been added to the code base, including functional-group and open-shell symmetry adapted perturbation theory, density-fitted coupled cluster with frozen natural orbitals, orbital-optimized perturbation and coupled-cluster methods (e.g., OO-MP2 and OO-LCCD), density-fitted multiconfigurational self-consistent field, density cumulant functional theory, algebraic-diagrammatic construction excited states, improvements to the geometry optimizer, and the "X2C" approach to relativistic corrections, among many other improvements.

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

An improved algorithm is presented for the evaluation of the (T) correction as a part of our local natural orbital (LNO) coupled-cluster singles and doubles with perturbative triples [LNO-CCSD(T)] scheme [Z. Rolik et al., J. Chem. Phys. 139, 094105 (2013)]. The new algorithm is an order of magnitude faster than our previous one and removes the bottleneck related to the calculation of the (T) contribution. First, a numerical Laplace transformed expression for the (T) fragment energy is introduced, which requires on average 3 to 4 times fewer floating point operations with negligible compromise in accuracy eliminating the redundancy among the evaluated triples amplitudes. Second, an additional speedup factor of 3 is achieved by the optimization of our canonical (T) algorithm, which is also executed in the local case. These developments can also be integrated into canonical as well as alternative fragmentation-based local CCSD(T) approaches with minor modifications. As it is demonstrated by our benchmark calculations, the evaluation of the new Laplace transformed (T) correction can always be performed if the preceding CCSD iterations are feasible, and the new scheme enables the computation of LNO-CCSD(T) correlation energies with at least triple-zeta quality basis sets for realistic three-dimensional molecules with more than 600 atoms and 12 000 basis functions in a matter of days on a single processor.

Reduced-cost linear-response CC2 method based on natural orbitals and natural auxiliary functions

A reduced-cost density fitting (DF) linear-response second-order coupled-cluster (CC2) method has been developed for the evaluation of excitation energies. The method is based on the simultaneous truncation of the molecular orbital (MO) basis and the auxiliary basis set used for the DF approximation. For the reduction of the size of the MO basis, state-specific natural orbitals (NOs) are constructed for each excited state using the average of the second-order Møller-Plesset (MP2) and the corresponding configuration interaction singles with perturbative doubles [CIS(D)] density matrices. After removing the NOs of low occupation number, natural auxiliary functions (NAFs) are constructed [M. Kállay, J. Chem. Phys. 141, 244113 (2014)], and the NAF basis is also truncated. Our results show that, for a triple-zeta basis set, about 60% of the virtual MOs can be dropped, while the size of the fitting basis can be reduced by a factor of five. This results in a dramatic reduction of the computational costs of the solution of the CC2 equations, which are in our approach about as expensive as the evaluation of the MP2 and CIS(D) density matrices. All in all, an average speedup of more than an order of magnitude can be achieved at the expense of a mean absolute error of 0.02 eV in the calculated excitation energies compared to the canonical CC2 results. Our benchmark calculations demonstrate that the new approach enables the efficient computation of CC2 excitation energies for excited states of all types of medium-sized molecules composed of up to 100 atoms with triple-zeta quality basis sets.

Evaluation of the restricted virtual space approximation in the algebraic-diagrammatic construction scheme for the polarization propagator to speed-up excited-state calculations

The applicability and limitations of the restricted virtual space (RVS) approximation within the algebraic-diagrammatic construction (ADC) scheme for the polarization propagator up to third order is evaluated. In RVS-ADC, not only the core but also a substantial amount of energetically high-lying virtual orbitals is restricted in excitation energy calculations of low-lying excited electronic states. Using octatetraene, indole, and pyridine as representative examples and different standard basis sets of triple-zeta quality, RVS-ADC(2) turns out to be highly useful and to have negligible effects on ππ* excited states. However, for nπ* or πσ* states, the RVS approximation is generally less reliable but better at third-order than second-order ADC level. In addition, a unified, basis-set independent, thus normalized virtual orbital threshold (value) is introduced, making the RVS approximation more controllable and a priori applicable. © 2017 Wiley Periodicals, Inc.

Analytic energy gradients for the coupled-cluster singles and doubles method with the density-fitting approximation

An efficient implementation is presented for analytic gradients of the coupled-cluster singles and doubles (CCSD) method with the density-fitting approximation, denoted DF-CCSD. Frozen core terms are also included. When applied to a set of alkanes, the DF-CCSD analytic gradients are significantly accelerated compared to conventional CCSD for larger molecules. The efficiency of our DF-CCSD algorithm arises from the acceleration of several different terms, which are designated as the "gradient terms": computation of particle density matrices (PDMs), generalized Fock-matrix (GFM), solution of the Z-vector equation, formation of the relaxed PDMs and GFM, back-transformation of PDMs and GFM to the atomic orbital (AO) basis, and evaluation of gradients in the AO basis. For the largest member of the alkane set (C10H22), the computational times for the gradient terms (with the cc-pVTZ basis set) are 2582.6 (CCSD) and 310.7 (DF-CCSD) min, respectively, a speed up of more than 8-folds. For gradient related terms, the DF approach avoids the usage of four-index electron repulsion integrals. Based on our previous study [U. Bozkaya, J. Chem. Phys. 141, 124108 (2014)], our formalism completely avoids construction or storage of the 4-index two-particle density matrix (TPDM), using instead 2- and 3-index TPDMs. The DF approach introduces negligible errors for equilibrium bond lengths and harmonic vibrational frequencies.

Benchmark Calculations of Three-Body Intermolecular Interactions and the Performance of Low-Cost Electronic Structure Methods

Many-body noncovalent interactions are increasingly important in large and/or condensed-phase systems, but the current understanding of how well various models predict these interactions is limited. Here, benchmark complete-basis set coupled cluster singles, doubles, and perturbative triples (CCSD(T)) calculations have been performed to generate a new test set for three-body intermolecular interactions. This "3B-69" benchmark set includes three-body interaction energies for 69 total trimer structures, consisting of three structures from each of 23 different molecular crystals. By including structures that exhibit a variety of intermolecular interactions and packing arrangements, this set provides a stringent test for the ability of electronic structure methods to describe the correct physics involved in the interactions. Both MP2.5 (the average of second- and third-order Møller-Plesset perturbation theory) and spin-component-scaled CCSD for noncovalent interactions (SCS-MI-CCSD) perform well. MP2 handles the polarization aspects reasonably well, but it omits three-body dispersion. In contrast, many widely used density functionals corrected with three-body D3 dispersion correction perform comparatively poorly. The primary difficulty stems from the treatment of exchange and polarization in the functionals rather than from the dispersion correction, though the three-body dispersion may also be moderately underestimated by the D3 correction.

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

The A24 data set (Řezáč 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.

Communication: resolving the three-body contribution to the lattice energy of crystalline benzene: benchmark results from coupled-cluster theory

Coupled-cluster theory including single, double, and perturbative triple excitations [CCSD(T)] has been applied to trimers that appear in crystalline benzene in order to resolve discrepancies in the literature about the magnitude of non-additive three-body contributions to the lattice energy. The present results indicate a non-additive three-body contribution of 0.89 kcal mol(-1), or 7.2% of the revised lattice energy of -12.3 kcal mol(-1). For the trimers for which we were able to compute CCSD(T) energies, we obtain a sizeable difference of 0.63 kcal mol(-1) between the CCSD(T) and MP2 three-body contributions to the lattice energy, confirming that three-body dispersion dominates over three-body induction. Taking this difference as an estimate of three-body dispersion for the closer trimers, and adding an Axilrod-Teller-Muto estimate of 0.13 kcal mol(-1) for long-range contributions yields an overall value of 0.76 kcal mol(-1) for three-body dispersion, a significantly smaller value than in several recent studies.