Symmetry Breaking Slows Convergence of the ADAPT Variational Quantum Eigensolver.

Because quantum simulation of molecular systems is expected to provide the strongest advantage over classical computing methods for systems exhibiting strong electron correlation, it is critical that the performance of VQEs be assessed for strongly correlated systems. For classical simulation, strong correlation often results in symmetry breaking of the Hartree-Fock reference, leading to Löwdin's well-known "symmetry dilemma", whereby accuracy in the energy can be increased by breaking spin or spatial symmetries. Here, we explore the impact of symmetry breaking on the performance of ADAPT-VQE using two strongly correlated systems: (i) the "fermionized" anisotropic Heisenberg model, where the anisotropy parameter controls the correlation in the system, and (ii) symmetrically stretched linear H4, where correlation increases with increasing H-H separation. In both of these cases, increasing the level of correlation of the system leads to spontaneous symmetry breaking (parity and S^2, respectively) of the mean-field solutions. We analyze the role that symmetry breaking in the reference states and orbital mappings of the fermionic Hamiltonians have in the compactness and performance of ADAPT-VQE. We observe that improving the energy of the reference states by breaking symmetry has a deleterious effect on ADAPT-VQE by increasing the length of the ansatz necessary for energy convergence and exacerbating the problem of "gradient troughs".

NewtonNet: a Newtonian message passing network for deep learning of interatomic potentials and forces.

We report a new deep learning message passing network that takes inspiration from Newton's equations of motion to learn interatomic potentials and forces. With the advantage of directional information from trainable force vectors, and physics-infused operators that are inspired by Newtonian physics, the entire model remains rotationally equivariant, and many-body interactions are inferred by more interpretable physical features. We test NewtonNet on the prediction of several reactive and non-reactive high quality ab initio data sets including single small molecules, a large set of chemically diverse molecules, and methane and hydrogen combustion reactions, achieving state-of-the-art test performance on energies and forces with far greater data and computational efficiency than other deep learning models.

A benchmark dataset for Hydrogen Combustion.

The generation of reference data for deep learning models is challenging for reactive systems, and more so for combustion reactions due to the extreme conditions that create radical species and alternative spin states during the combustion process. Here, we extend intrinsic reaction coordinate (IRC) calculations with ab initio MD simulations and normal mode displacement calculations to more extensively cover the potential energy surface for 19 reaction channels for hydrogen combustion. A total of ∼290,000 potential energies and ∼1,270,000 nuclear force vectors are evaluated with a high quality range-separated hybrid density functional, ωB97X-V, to construct the reference data set, including transition state ensembles, for the deep learning models to study hydrogen combustion reaction.

Exploring the Limits of Second- and Third-Order Møller-Plesset Perturbation Theories for Noncovalent Interactions: Revisiting MP2.5 and Assessing the Importance of Regularization and Reference Orbitals.

This work systematically assesses the influence of reference orbitals, regularization, and scaling on the performance of second- and third-order Møller-Plesset perturbation theory wave function methods for noncovalent interactions (NCIs). Testing on 19 data sets (A24, DS14, HB15, HSG, S22, X40, HW30, NC15, S66, AlkBind12, CO2Nitrogen16, HB49, Ionic43, TA13, XB18, Bauza30, CT20, XB51, and Orel26rad) covers a wide range of different NCIs including hydrogen bonding, dispersion, and halogen bonding. Inclusion of potential energy surfaces from different hydrogen bonds and dispersion-bound complexes gauges accuracy for nonequilibrium geometries. Fifteen methods are tested. In notation where nonstandard choices of orbitals are denoted as methods:orbitals, these are MP2, κ-MP2, SCS-MP2, OOMP2, κ-OOMP2, MP3, MP2.5, MP3:OOMP2, MP2.5:OOMP2, MP3:κ-OOMP2, MP2.5:κ-OOMP2, κ-MP3:κ-OOMP2, κ-MP2.5:κ-OOMP2, MP3:ωB97X-V, and MP2.5:ωB97X-V. Furthermore, we compare these methods to the ωB97M-V and B3LYP-D3 density functionals, as well as CCSD. We find that the κ-regularization (κ = 1.45 au was used throughout) improves the energetics in almost all data sets for both MP2 (in 17 out of 19 data sets) and OOMP2 (16 out of 19). The improvement is significant (e.g., the root-mean-square deviation (RMSD) for the S66 data set is 0.29 kcal/mol for κ-OOMP2 versus 0.67 kcal/mol for MP2) and for interactions between stable closed-shell molecules, not strongly dependent on the reference orbitals. Scaled MP3 (with a factor of 0.5) using κ-OOMP2 reference orbitals (MP2.5:κ-OOMP2) provides significantly more accurate results for NCIs across all data sets with noniterative O(N6) scaling (S66 data set RMSD: 0.10 kcal/mol). Across the entire data set of 356 points, the improvement over standard MP2.5 is approximately a factor of 2: RMSD for MP3:κ-OOMP2 is 0.25 vs 0.50 kcal/mol for MP2.5. The use of high-quality density functional reference orbitals (ωB97X-V) also significantly improves the results of MP2.5 for NCI over a Hartree-Fock orbital reference. All our assessments and conclusions are based on the use of the medium-sized aug-cc-pVTZ basis to yield results that are directly compared against complete basis set limit reference values.

Polishing the Gold Standard: The Role of Orbital Choice in CCSD(T) Vibrational Frequency Prediction.

While CCSD(T) with spin-restricted Hartree-Fock (RHF) orbitals has long been lauded for its ability to accurately describe closed-shell interactions, the performance of CCSD(T) on open-shell species is much more erratic, especially when using a spin-unrestricted HF (UHF) reference. Previous studies have shown improved treatment of open-shell systems when a non-HF set of molecular orbitals, like Brueckner or Kohn-Sham density functional theory (DFT) orbitals, is used as a reference. Inspired by the success of regularized orbital-optimized second-order Møller-Plesset perturbation theory (κ-OOMP2) orbitals as reference orbitals for MP3, we investigate the use of κ-OOMP2 orbitals and various DFT orbitals as reference orbitals for CCSD(T) calculations of the corrected ground-state harmonic vibrational frequencies of a set of 36 closed-shell (29 neutrals, 6 cations, 1 anion) and 59 open-shell diatomic species (38 neutrals, 15 cations, 6 anions). The aug-cc-pwCVTZ basis set is used for all calculations. The use of κ-OOMP2 orbitals in this context alleviates difficult cases observed for both UHF orbitals and OOMP2 orbitals. Removing two multireference systems and 12 systems with ambiguous experimental data leaves a pruned data set. Overall performance on the pruned data set highlights CCSD(T) with a B97 orbital reference (CCSD(T):B97), CCSD(T) with a κ-OOMP2 orbital reference (CCSD(T):κ-OOMP2), and CCSD(T) with a B97M-rV orbital reference (CCSD(T):B97M-rV) with RMSDs of 8.48 cm-1, and 8.50 cm-1, and 8.75 cm-1 respectively, outperforming CCSD(T):UHF by nearly a factor of 5. Moreover, the performance on the closed- and open-shell subsets shows these methods are able to treat open-shell and closed-shell systems with comparable accuracy and robustness. CCSD(T) with RHF orbitals is seen to improve upon UHF for the closed-shell species, while spatial symmetry breaking in a number of restricted open-shell HF (ROHF) references leads CCSD(T) with ROHF reference orbitals to exhibit the poorest statistical performance of all methods surveyed for open-shell species. The use of κ-OOMP2 orbitals has also proven useful in diagnosing multireference character that can hinder the reliability of CCSD(T).

Third-Order Møller-Plesset Theory Made More Useful? The Role of Density Functional Theory Orbitals.

The practical utility of Møller-Plesset (MP) perturbation theory is severely constrained by the use of Hartree-Fock (HF) orbitals. It has recently been shown that the use of regularized orbital-optimized MP2 orbitals and scaling of MP3 energy could lead to a significant reduction in MP3 error [Bertels, L. W.; J. Phys. Chem. Lett. 2019, 10, 4170 4176]. In this work, we examine whether density functional theory (DFT)-optimized orbitals can be similarly employed to improve the performance of MP theory at both the MP2 and MP3 levels. We find that the use of DFT orbitals leads to significantly improved performance for prediction of thermochemistry, barrier heights, noncovalent interactions, and dipole moments relative to the standard HF-based MP theory. Indeed, MP3 (with or without scaling) with DFT orbitals is found to surpass the accuracy of coupled-cluster singles and doubles (CCSD) for several data sets. We also found that the results are not particularly functional sensitive in most cases (although range-separated hybrid functionals with low delocalization error perform the best). MP3 based on DFT orbitals thus appears to be an efficient, noniterative O(N6) scaling wave-function approach for single-reference electronic structure computations. Scaled MP2 with DFT orbitals is also found to be quite accurate in many cases, although modern double hybrid functionals are likely to be considerably more accurate.

Benchmarking the Performance of the ReaxFF Reactive Force Field on Hydrogen Combustion Systems.

A thorough understanding of the kinetics and dynamics of combusting mixtures is of considerable interest, especially in regimes beyond the reach of current experimental validation. The ReaxFF reactive force field method has provided a way to simulate large-scale systems of hydrogen combustion via a parametrized potential that can simulate bond breaking. This modeling approach has been applied to hydrogen combustion, as well as myriad other reactive chemical systems. In this work, we benchmark the performance of several common parametrizations of this potential against higher-level quantum mechanical (QM) approaches. We demonstrate instances where these parametrizations of the ReaxFF potential fail both quantitatively and qualitatively to describe reactive events relevant for hydrogen combustion systems.

Kohn-Sham Density Functional Theory with Complex, Spin-Restricted Orbitals: Accessing a New Class of Densities without the Symmetry Dilemma.

We show that using complex, spin-restricted orbitals in Kohn-Sham (KS) density functional theory allows one to access a new class of densities that is not accessible by either spin-restricted (RKS) or spin-unrestricted (UKS) orbitals. We further show that the real part of a complex RKS (CRKS) density matrix can be nonidempotent when the imaginary part of the density matrix is not zero. Using CRKS orbitals shows significant improvements in the triplet-singlet gaps of a benchmark set, called TS12, for well-established, widely used density functionals. Moreover, it was shown that RKS and UKS yield qualitatively wrong charge densities and spin densities, respectively, leading to worse energetics. We demonstrate that representative modern density functionals show surprisingly no improvement even with a qualitatively more accurate density from CRKS orbitals. To this end, our work not only provides a way to escape the symmetry dilemma whenever there exists a CRKS solution, but also suggests a new route to design better approximate density functionals.

Gas phase formation of c-SiC3 molecules in the circumstellar envelope of carbon stars.

Complex organosilicon molecules are ubiquitous in the circumstellar envelope of the asymptotic giant branch (AGB) star IRC+10216, but their formation mechanisms have remained largely elusive until now. These processes are of fundamental importance in initiating a chain of chemical reactions leading eventually to the formation of organosilicon molecules-among them key precursors to silicon carbide grains-in the circumstellar shell contributing critically to the galactic carbon and silicon budgets with up to 80% of the ejected materials infused into the interstellar medium. Here we demonstrate via a combined experimental, computational, and modeling study that distinct chemistries in the inner and outer envelope of a carbon star can lead to the synthesis of circumstellar silicon tricarbide (c-SiC3) as observed in the circumstellar envelope of IRC+10216. Bimolecular reactions of electronically excited silicon atoms (Si(1D)) with allene (H2CCCH2) and methylacetylene (CH3CCH) initiate the formation of SiC3H2 molecules in the inner envelope. Driven by the stellar wind to the outer envelope, subsequent photodissociation of the SiC3H2 parent operates the synthesis of the c-SiC3 daughter species via dehydrogenation. The facile route to silicon tricarbide via a single neutral-neutral reaction to a hydrogenated parent molecule followed by photochemical processing of this transient to a bare silicon-carbon molecule presents evidence for a shift in currently accepted views of the circumstellar organosilicon chemistry, and provides an explanation for the previously elusive origin of circumstellar organosilicon molecules that can be synthesized in carbon-rich, circumstellar environments.

Third-Order Møller-Plesset Perturbation Theory Made Useful? Choice of Orbitals and Scaling Greatly Improves Accuracy for Thermochemistry, Kinetics, and Intermolecular Interactions.

We develop and test methods that include second- and third-order perturbation theory (MP3) using orbitals obtained from regularized orbital-optimized second-order perturbation theory, κ-OOMP2, denoted as MP3:κ-OOMP2. Testing MP3:κ-OOMP2 shows RMS errors that are 1.7-5 times smaller than those of MP3 across 7 data sets. To do still better, empirical training of the scaling factors for the second- and third-order correlation energies and the regularization parameter on one of those data sets led to an unregularized scaled (c2 = 1.0; c3 = 0.8) denoted as MP2.8:κ-OOMP2. MP2.8:κ-OOMP2 yields significant additional improvement over MP3:κ-OOMP2 in 4 of 6 test data sets on thermochemistry, kinetics, and noncovalent interactions. Remarkably, these two methods outperform coupled cluster with singles and doubles in 5 of the 7 data sets considered, at greatly reduced cost (no O(N6) iterations).

A Combined Experimental and Theoretical Study on the Formation of the 2-Methyl-1-silacycloprop-2-enylidene Molecule via the Crossed Beam Reactions of the Silylidyne Radical (SiH; X(2)Π) with Methylacetylene (CH3CCH; X(1)A1) and D4-Methylacetylene (CD3CCD; X(1)A1).

The bimolecular gas-phase reactions of the ground-state silylidyne radical (SiH; X(2)Π) with methylacetylene (CH3CCH; X(1)A1) and D4-methylacetylene (CD3CCD; X(1)A1) were explored at collision energies of 30 kJ mol(-1) under single-collision conditions exploiting the crossed molecular beam technique and complemented by electronic structure calculations. These studies reveal that the reactions follow indirect scattering dynamics, have no entrance barriers, and are initiated by the addition of the silylidyne radical to the carbon-carbon triple bond of the methylacetylene molecule either to one carbon atom (C1; [i1]/[i2]) or to both carbon atoms concurrently (C1-C2; [i3]). The collision complexes [i1]/[i2] eventually isomerize via ring-closure to the c-SiC3H5 doublet radical intermediate [i3], which is identified as the decomposing reaction intermediate. The hydrogen atom is emitted almost perpendicularly to the rotational plane of the fragmenting complex resulting in a sideways scattering dynamics with the reaction being overall exoergic by -12 ± 11 kJ mol(-1) (experimental) and -1 ± 3 kJ mol(-1) (computational) to form the cyclic 2-methyl-1-silacycloprop-2-enylidene molecule (c-SiC3H4; p1). In line with computational data, experiments of silylidyne with D4-methylacetylene (CD3CCD; X(1)A1) depict that the hydrogen is emitted solely from the silylidyne moiety but not from methylacetylene. The dynamics are compared to those of the related D1-silylidyne (SiD; X(2)Π)-acetylene (HCCH; X(1)Σg(+)) reaction studied previously in our group, and from there, we discovered that the methyl group acts primarily as a spectator in the title reaction. The formation of 2-methyl-1-silacycloprop-2-enylidene under single-collision conditions via a bimolecular gas-phase reaction augments our knowledge of the hitherto poorly understood silylidyne (SiH; X(2)Π) radical reactions with small hydrocarbon molecules leading to the synthesis of organosilicon molecules in cold molecular clouds and in carbon-rich circumstellar envelopes.

Combined Experimental and Theoretical Study on the Formation of the Elusive 2-Methyl-1-silacycloprop-2-enylidene Molecule under Single Collision Conditions via Reactions of the Silylidyne Radical (SiH; X(2)Π) with Allene (H2CCCH2; X(1)A1) and D4-Allene (D2CCCD2; X(1)A1).

The crossed molecular beam reactions of the ground-state silylidyne radical (SiH; X(2)Π) with allene (H2CCCH2; X(1)A1) and D4-allene (D2CCCD2; X(1)A1) were carried out at collision energies of 30 kJ mol(-1). Electronic structure calculations propose that the reaction of silylidyne with allene has no entrance barrier and is initiated by silylidyne addition to the π electron density of allene either to one carbon atom (C1/C2) or to both carbon atoms simultaneously via indirect (complex forming) reaction dynamics. The initially formed addition complexes isomerize via two distinct reaction pathways, both leading eventually to a cyclic SiC3H5 intermediate. The latter decomposes through a loose exit transition state via an atomic hydrogen loss perpendicularly to the plane of the decomposing complex (sideways scattering) in an overall exoergic reaction (experimentally: -19 ± 13 kJ mol(-1); computationally: -5 ± 3 kJ mol(-1)). This hydrogen loss yields the hitherto elusive 2-methyl-1-silacycloprop-2-enylidene molecule (c-SiC3H4), which can be derived from the closed-shell cyclopropenylidene molecule (c-C3H2) by replacing a hydrogen atom with a methyl group and the carbene carbon atom by the isovalent silicon atom. The synthesis of the 2-methyl-1-silacycloprop-2-enylidene molecule in the bimolecular gas-phase reaction of silylidyne with allene enriches our understanding toward the formation of organosilicon species in the gas phase of the interstellar medium in particular via exoergic reactions of no entrance barrier. This facile route to 2-methyl-1-silacycloprop-2-enylidene via a silylidyne radical reaction with allene opens up a versatile approach to form hitherto poorly characterized silicon-bearing species in extraterrestrial environments; this reaction class might represent the missing link, leading from silicon-bearing radicals via organosilicon chemistry eventually to silicon-carbon-rich interstellar grains even in cold molecular clouds where temperatures are as low as 10 K.

Accurate prediction of diradical chemistry from a single-reference density-matrix method: Model application to the bicyclobutane to gauche-1,3-butadiene isomerization.

Multireference correlation in diradical molecules can be captured by a single-reference 2-electron reduced-density-matrix (2-RDM) calculation with only single and double excitations in the 2-RDM parametrization. The 2-RDM parametrization is determined by N-representability conditions that are non-perturbative in their treatment of the electron correlation. Conventional single-reference wave function methods cannot describe the entanglement within diradical molecules without employing triple- and potentially even higher-order excitations of the mean-field determinant. In the isomerization of bicyclobutane to gauche-1,3-butadiene the parametric 2-RDM (p2-RDM) method predicts that the diradical disrotatory transition state is 58.9 kcal/mol above bicyclobutane. This barrier is in agreement with previous multireference calculations as well as recent Monte Carlo and higher-order coupled cluster calculations. The p2-RDM method predicts the Nth natural-orbital occupation number of the transition state to be 0.635, revealing its diradical character. The optimized geometry from the p2-RDM method differs in important details from the complete-active-space self-consistent-field geometry used in many previous studies including the Monte Carlo calculation.