Reducing the Runtime of Fault-Tolerant Quantum Simulations in Chemistry through Symmetry-Compressed Double Factorization.

Quantum phase estimation based on qubitization is the state-of-the-art fault-tolerant quantum algorithm for computing ground-state energies in chemical applications. In this context, the 1-norm of the Hamiltonian plays a fundamental role in determining the total number of required iterations and also the overall computational cost. In this work, we introduce the symmetry-compressed double factorization (SCDF) approach, which combines a CDF of the Hamiltonian with the symmetry shift technique, significantly reducing the 1-norm value. The effectiveness of this approach is demonstrated numerically by considering various benchmark systems, including the FeMoco molecule, cytochrome P450, and hydrogen chains of different sizes. To compare the efficiency of SCDF to other methods in absolute terms, we estimate Toffoli gate requirements, which dominate the execution time on fault-tolerant quantum computers. For the systems considered here, SCDF leads to a sizable reduction of the Toffoli gate count in comparison to other variants of DF or even tensor hypercontraction, which is usually regarded as the most efficient approach for qubitization.

Approaching the basis set limit in Gaussian-orbital-based periodic calculations with transferability: Performance of pure density functionals for simple semiconductors.

Simulating solids with quantum chemistry methods and Gaussian-type orbitals (GTOs) has been gaining popularity. Nonetheless, there are few systematic studies that assess the basis set incompleteness error (BSIE) in these GTO-based simulations over a variety of solids. In this work, we report a GTO-based implementation for solids and apply it to address the basis set convergence issue. We employ a simple strategy to generate large uncontracted (unc) GTO basis sets that we call the unc-def2-GTH sets. These basis sets exhibit systematic improvement toward the basis set limit as well as good transferability based on application to a total of 43 simple semiconductors. Most notably, we found the BSIE of unc-def2-QZVP-GTH to be smaller than 0.7 mEh per atom in total energies and 20 meV in bandgaps for all systems considered here. Using unc-def2-QZVP-GTH, we report bandgap benchmarks of a combinatorially designed meta-generalized gradient approximation (mGGA) functional, B97M-rV, and show that B97M-rV performs similarly (a root-mean-square-deviation of 1.18 eV) to other modern mGGA functionals, M06-L (1.26 eV), MN15-L (1.29 eV), and Strongly Constrained and Appropriately Normed (SCAN) (1.20 eV). This represents a clear improvement over older pure functionals such as local density approximation (1.71 eV) and Perdew-Burke-Ernzerhof (PBE) (1.49 eV), although all these mGGAs are still far from being quantitatively accurate. We also provide several cautionary notes on the use of our uncontracted bases and on future research on GTO basis set development for solids.

Compressed intramolecular dispersion interactions.

The feasibility of the compression of localized virtual orbitals is explored in the context of intramolecular long-range dispersion interactions. Singular value decomposition (SVD) of coupled cluster doubles amplitudes associated with the dispersion interactions is analyzed for a number of long-chain systems, including saturated and unsaturated hydrocarbons and a silane chain. Further decomposition of the most important amplitudes obtained from these SVDs allows for the analysis of the dispersion-specific virtual orbitals that are naturally localized. Consistent with previous work on intermolecular dispersion interactions in dimers, it is found that three important geminals arise and account for the majority of dispersion interactions at the long range, even in the many body intramolecular case. Furthermore, it is shown that as few as three localized virtual orbitals per occupied orbital can be enough to capture all pairwise long-range dispersion interactions within a molecule.

Assessing Electronic Structure Methods for Long-Range Three-Body Dispersion Interactions: Analysis and Calculations on Well-Separated Metal Atom Trimers.

Three-body dispersion interactions are much weaker than their two-body counterpart. However, their importance grows quickly as the number of interacting monomers rises. To explore the numerical performance of correlation methods for long-range three-body dispersion, we performed calculations on eight very simple dispersion-dominated model metal trimers: Na3, Mg3, Zn3, Cd3, Hg3, Cu3, Ag3, and Au3. One encouraging aspect is that relatively small basis sets of augmented triple-ζ size appear to be adequate for three-body dispersion in the long-range. Coupled cluster calculations were performed at high levels to assess MP3, CCSD, CCSD(T), empirical density functional theory dispersion (D3), and the many-body dispersion (MBD) approach. We found that the accuracy of CCSD(T) was generally significantly lower than for two-body interactions, with errors sometimes reaching 20% in the investigated systems, while CCSD and particularly MP3 were generally more erratic. MBD is found to perform better than D3 at large distances, whereas the opposite is true at shorter distances. When computing reference numbers for three-body dispersion, care should be taken to appropriately represent the effect of the connected triple excitations, which are significant in most cases and incompletely approximated by CCSD(T).

Water Bridges Conduct Sequential Proton Transfer in Photosynthetic Oxygen Evolution.

Proton transfer using water bridges has been observed in bulk water, acid-base reactions, and several proton-translocating biological systems. In the photosynthetic water-oxidizing enzyme, photosystem II (PSII), protons from substrate water are transferred 35 Å from the Mn4CaO5 catalytic site to the chloroplast lumen. This process leads to acidification of the lumen and ATP synthesis. Water oxidation occurs in a flash-induced, five-step S n state cycle; acetate is a chloride-dependent inhibitor of the S2 to S3 step of this cycle. Here, we study the effect of acetate on a previous step of the cycle, the S1 to S2 transition, using reaction-induced infrared spectroscopy. PSII was isolated from spinach, and experiments were conducted at pH 7.5, using 532 nm laser flashes to advance the cycle from the dark-adapted state S1 to the S2 state. Isotope-editing of acetate reveals direct contributions to the S2-minus-S1 infrared spectrum consistent with protonation of bound acetate in PSII. In the acetate-derived S2-minus-S1 PSII spectra, an accompanying decrease in the intensity of a 2830 cm-1 band is observed when compared to the chloride control. The 2830 cm-1 band has been assigned previously to a stretching vibration of an internal, hydrated hydronium ion, W n+. Density functional studies of a catalytic site model predict the spontaneous transfer of a proton from this internal hydronium ion to acetate, when acetate is substituted at a chloride-binding site. Taken together, the results show that the mechanism of PSII proton transfer at pH 7.5 involves proton hopping through an internal, water-containing network.

Understanding Non-Covalent Interactions: Correlated Energy Decomposition Analysis and Applications to Halogen Bonding.

Non-covalent interactions play a primordial role in chemistry. Beyond their quantification, the detailed understanding of their physical processes is necessary to rationalize chemical trends and improve designs of chemical systems. Energy decomposition analyses allow detailed insight into non-covalent interactions by extracting electrostatics, Pauli repulsion, polarization, dispersion and charge transfer components from interaction energies. Recent work has demonstrated that electronic correlation influenced significantly all of these energy components, whereas previous decompositions only partitioned correlation between dispersion and charge transfer. The MP2 energy decomposition analysis with Absolutely Localized Molecular Orbitals (MP2 ALMO-EDA) takes these results fully into account and offers a correlation correction for each extracted component. A recent detailed investigation of the CCSD dispersion energy showed that a small number of virtual orbitals is sufficient to describe dispersion interactions accurately in the long-range, which potentially offers a basis-set independent definition of dispersion. Finally, we present an application of MP2 ALMO-EDA to a series of unusual halogen bonding complexes where charge transfer dominates over the electrostatic σ-hole interaction.

Chloride Maintains a Protonated Internal Water Network in the Photosynthetic Oxygen Evolving Complex.

In photosystem II (PSII), water oxidation occurs at a Mn4CaO5 cluster and results in production of molecular oxygen. The Mn4CaO5 cluster cycles among five oxidation states, called Sn states. As a result, protons are released at the metal cluster and transferred through a 35 Å hydrogen-bonding network to the lumen. At 283 K, an infrared band at 2830 cm-1 is assigned to an internal solvated hydronium ion via H218O solvent exchange. This result is similar to a previous report at 263 K. Computations on an oxygen evolving complex model predict that chloride can stabilize a hydronium ion on a network of nine water molecules. In this model, a H3O+ stretching mode at 2738 cm-1 is predicted to shift to higher frequency with bromide and to lower frequency with nitrate substitution. The calculated frequencies were compared to S2-minus-S1 reaction-induced Fourier transform infrared spectra acquired from chloride-, bromide-, or nitrate-containing PSII samples, which were active in oxygen evolution. As predicted, the frequency of the 2830 cm-1 band shifted to higher energy with bromide and to lower energy with nitrate substitution. These results support the conclusion that an internal hydronium ion and chloride play a direct role in an internal proton transfer event during the S1-to-S2 transition.

Compressed representation of dispersion interactions and long-range electronic correlations.

The description of electron correlation in quantum chemistry often relies on multi-index quantities. Here, we examine a compressed representation of the long-range part of electron correlation that is associated with dispersion interactions. For this purpose, we perform coupled-cluster singles and doubles (CCSD) computations on localized orbitals, and then extract the portion of CCSD amplitudes corresponding to dispersion energies. Using singular value decomposition, we uncover that a very compressed representation of the amplitudes is possible in terms of occupied-virtual geminal pairs located on each monomer. These geminals provide an accurate description of dispersion energies at medium and long distances. The corresponding virtual orbitals are examined by further singular value decompositions of the geminals. We connect each component of the virtual space to the multipole expansion of dispersion energies. Our results are robust with respect to basis set change and hold for systems as large as the benzene-methane dimer. This compressed representation of dispersion energies paves the way to practical and accurate approximations for dispersion, for example, in local correlation methods.

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.

Density-fitted open-shell symmetry-adapted perturbation theory and application to π-stacking in benzene dimer cation and ionized DNA base pair steps.

Symmetry-Adapted Perturbation Theory (SAPT) is one of the most popular approaches to energy component analysis of non-covalent interactions between closed-shell systems, yielding both accurate interaction energies and meaningful interaction energy components. In recent years, the full open-shell equations for SAPT up to second-order in the intermolecular interaction and zeroth-order in the intramolecular correlation (SAPT0) were published [P. S. Zuchowski et al., J. Chem. Phys. 129, 084101 (2008); M. Hapka et al., ibid. 137, 164104 (2012)]. Here, we utilize density-fitted electron repulsion integrals to produce an efficient computational implementation. This approach is used to examine the effect of ionization on π-π interactions. For the benzene dimer radical cation, comparison against reference values indicates a good performance for open-shell SAPT0, except in cases with substantial charge transfer. For π stacking between hydrogen-bonded pairs of nucleobases, dispersion interactions still dominate binding, in spite of the creation of a positive charge.

Intramolecular symmetry-adapted perturbation theory with a single-determinant wavefunction.

We introduce an intramolecular energy decomposition scheme for analyzing non-covalent interactions within molecules in the spirit of symmetry-adapted perturbation theory (SAPT). The proposed intra-SAPT approach is based upon the Chemical Hamiltonian of Mayer [Int. J. Quantum Chem. 23(2), 341-363 (1983)] and the recently introduced zeroth-order wavefunction [J. F. Gonthier and C. Corminboeuf, J. Chem. Phys. 140(15), 154107 (2014)]. The scheme decomposes the interaction energy between weakly bound fragments located within the same molecule into physically meaningful components, i.e., electrostatic-exchange, induction, and dispersion. Here, we discuss the key steps of the approach and demonstrate that a single-determinant wavefunction can already deliver a detailed and insightful description of a wide range of intramolecular non-covalent phenomena such as hydrogen bonds, dihydrogen contacts, and π - π stacking interactions. Intra-SAPT is also used to shed the light on competing intra- and intermolecular interactions.

Communication: Practical intramolecular symmetry adapted perturbation theory via Hartree-Fock embedding.

We develop a simple methodology for the computation of symmetry-adapted perturbation theory (SAPT) interaction energy contributions for intramolecular noncovalent interactions. In this approach, the local occupied orbitals of the total Hartree-Fock (HF) wavefunction are used to partition the fully interacting system into three chemically identifiable units: the noncovalent fragments A and B and a covalent linker C. Once these units are identified, the noninteracting HF wavefunctions of the fragments A and B are separately optimized while embedded in the HF wavefunction of C, providing the dressed zeroth order wavefunctions for A and B in the presence of C. Standard two-body SAPT (particularly SAPT0) is then applied between the relaxed wavefunctions for A and B. This intramolecular SAPT procedure is found to be remarkably straightforward and efficient, as evidenced by example applications ranging from diols to hexaphenyl-ethane derivatives.

Ligand-controlled regiodivergent pathways of rhodium(III)-catalyzed dihydroisoquinolone synthesis: experimental and computational studies of different cyclopentadienyl ligands.

Rh(III) -catalyzed directed C-H functionalizations of arylhydroxamates have become a valuable synthetic tool. To date, the regioselectivity of the insertion of the unsaturated acceptor into the common cyclometalated intermediate was dependent solely on intrinsic substrate control. Herein, we report two different catalytic systems that allow the selective formation of regioisomeric 3-aryl dihydroisoquinolones and previously inaccessible 4-aryl dihydroisoquinolones under full catalyst control. The differences in the catalysts are computationally examined using density functional theory and transition state theory of different possible pathways to elucidate key contributing factors leading to the regioisomeric products. The stabilities of the initially formed rhodium complex styrene adducts, as well as activation barrier differences for the migratory insertion, were identified as key contributing factors for the regiodivergent pathways.

Quantification and analysis of intramolecular interactions.

Non-covalent interactions play a prominent role in chemistry and biology. While a myriad of theoretical methods have been devised to quantify and analyze intermolecular interactions, the theoretical toolbox for the intramolecular analogues is much scarcer. Yet interactions within molecules govern fundamental phenomena as illustrated by the energetic differences between structural isomers. Their accurate quantification is of utmost importance. This paper gives an overview of the most common approaches able to probe intramolecular interactions and stresses both their characteristics and limitations. We finally introduce our recent theoretical approach, which represents the first step towards the development of an intramolecular version of Symmetry-Adapted Perturbation Theory (SAPT).

Adjusting the Local Arrangement of π-Stacked Oligothiophenes through Hydrogen Bonds: A Viable Route to Promote Charge Transfer.

We show that substituting quaterthiophene cores with strong H-bond aggregators, such as urea groups, provides an efficient way to adjust the mutual in-plane displacements of the semiconducting units and promote charge transfer. Our 2-D structure-property mapping reveals that the insertion of substituents induces up to 2.0 Å longitudinal and transversal displacements between the π-conjugated moieties. Some of these relative displacements lead to improved cofacial orbital overlaps that are otherwise inaccessible due to Pauli repulsion. Our results also emphasize that the fine-tuning of in-plane displacements is more effective than achieving "tighter" packing to promote charge-transfer properties.

π-Depletion as a criterion to predict π-stacking ability.

The screening of molecular targets benefits from design criteria, which can identify the most promising candidates. We demonstrate that π-depleted polyaromatic molecules present superior π-stacking ability. This realization is quantified using a computational criterion, LOLIPOP, that detects ideal π-conjugated frameworks. The utility of LOLIPOP is illustrated by identifying tailored chemosensors.

Quantification of "fuzzy" chemical concepts: a computational perspective.

Chemists recurrently utilize "fuzzy" chemical concepts (e.g. atomic charges, the chemical bond, strain, aromaticity, branching, etc.), which lack unique quantitative assessments but, nonetheless, are frequently employed as tools for understanding the intricacies of chemical behaviour. This tutorial review provides an overview of the computational schemes specifically developed to quantify four of the most commonly employed, yet debated, chemical concepts: the chemical bond, atomic charges, (hyper)conjugation, and molecular strain. The enhanced knowledge gained from these schemes not only helps in the depiction of molecules with unique properties, but also provides breadth to our fundamental understanding of chemistry. Nevertheless, the numerous existing methodologies often result in different interpretations that culminate in discrepancies. Through recent examples in the literature, guidelines are provided which illustrate the strengths and weaknesses of various schemes for each individual concept.

Four-electron oxygen reduction by tetrathiafulvalene.

The four-electron reduction of oxygen by tetrathiafulvalene (TTF) in acidified 1,2-dichloroethane and at the acidified water/1,2-dichloroethane interface has been observed. Spectroscopy and ion transfer voltammetry results suggest that the reaction proceeds by the fast protonation of TTF followed by the 4-electron reduction of oxygen to form water. Electronic structure computations give evidence of the formation of a helical tetramer assembly ([TTF(4)H(2)](2+)) of two protonated TTF and two neutral TTF molecules. The protonated tetramer is potentially able to deliver the four electrons needed for the oxygen reduction. The production of water was corroborated by (1)H NMR analysis.

Branched alkanes have contrasting stabilities.

Bond separation reactions of highly branched alkanes are used to assess (de)stabilizing interactions associated with various 1,3-nonbonded substituent patterns. While n- and singly methylated alkanes show positive bond separation energies (BSEs), which increase systematically along the series, permethylated alkanes are characterized by decreasing BSEs. Analysis shows that singly methylated alkanes are more stabilized than linear alkane chains and that the unique destabilizing feature of permethylated alkanes arises from the close proximity of bulky methyl groups causing highly distorted geometries along the carbon backbone.