PYSCF is a Python-based general-purpose electronic structure platform that both supports first-principles simulations of molecules and solids, as well as accelerates the development of new methodology and complex computational workflows. The present paper explains the design and philosophy behind PYSCF that enables it to meet these twin objectives. With several case studies, we show how users can easily implement their own methods using PYSCF as a development environment. We then summarize the capabilities of PYSCF for molecular and solid-state simulations. Finally, we describe the growing ecosystem of projects that use PYSCF across the domains of quantum chemistry, materials science, machine learning and quantum information science.

Alkene ozonolysis is a major source of hydroxyl radical (*OH), the most important oxidant in the troposphere. Previous experimental and computational work suggests that for many alkenes the measured *OH yields should be attributed to the combined impact of both chemically activated and thermalized syn-alkyl Criegee intermediates (CIs), even though the thermalized CI should be susceptible to trapping by molecules such as water. We have used RRKM/master equation and variational transition state theory calculations to quantify the competition between unimolecular isomerization and bimolecular hydration reactions for the syn and anti acetaldehyde oxide formed in trans-2-butene ozonolysis and for the CIs formed in isoprene ozonolysis possessing syn-methyl groups. Statistical rate theory calculations were based on quantum chemical data provided by the B3LYP, QCISD, and multicoefficient G3 methods, and thermal rate constants were corrected for tunneling effects using the Eckart method. At tropospheric temperatures and pressures, all thermalized CIs with syn-methyl groups are predicted to undergo 1,4-hydrogen shifts from 2 to 8 orders of magnitude faster than they react with water monomer at its saturation number density. For thermalized anti acetaldehyde oxide, the rates of dioxirane formation and hydration should be comparable.

Density matrix embedding theory (DMET) is a fully quantum-mechanical embedding method which shows great promise as a method of defeating the inherent exponential cost scaling of multiconfigurational wave function-based calculations by breaking large systems into smaller, coupled subsystems. However, we recently [JCTC 2018[JCTC , 14, 1960 encountered evidence that the approximate single-determinantal bath picture inherent to DMET is sometimes problematic when the complete active space self-consistent field (CASSCF) is used as a solver and the method is applied to realistic models of strongly-correlated molecules. Here, we show this problem can be defeated by generalizing DMET to use a multiconfigurational wave function as a bath without sacrificing practically attractive features of DMET, such as a secondquantization form of the embedded subsystem Hamiltonian, by dividing the active space into unentangled active subspaces each localized to one fragment. We introduce the term localized active space (LAS) to refer to this kind of wave function. The LAS bath wave function 1 arXiv:1810.03266v1 [physics.chem-ph] 8 Oct 2018can be obtained by the DMET algorithm itself in a self-consistent manner, and we refer to this approach, introduced here for the first time, as the localized active space self-consistent field (LASSCF) method. LASSCF exploits a modified DMET algorithm, but it requires no ambiguous error function minimization, produces a whole-molecule wave function with exact embedding, is variational, and it reproduces full-molecule CASSCF in cases where comparable DMET calculations fail. Our results for test calculations on the nitrogen double-bond dissociation potential energy curves of several diazene molecules suggest that LASSCF can be an appropriate starting point for a perturbative treatment. Outside of the context of embedding, the LAS wave function is inherently an attractive alternative to a CAS wave function because of its favorable cost scaling, which is exponential only with respect to the size of individual fragment active subspaces, rather than the whole active space of the entire system.

The atmospheric oxidation of sulfur dioxide by the parent and dimethyl Criegee intermediates (CIs) may be an important source of sulfuric acid aerosol, which has a large impact on radiative forcing and therefore upon climate. A number of computational studies have considered how the CH2OOS(O)O heteroozonide (HOZ) adduct formed in the CI + SO2 reaction converts SO2 to SO3. In this work we use the CBS-QB3 quantum chemical method along with equation-of-motion spin-flip CCSD(dT) and MCG3 theories to reveal new details regarding the formation and decomposition of the endo and exo conformers of the HOZ. Although ∼75% of the parent CI + SO2 reaction is initiated by formation of the exo HOZ, hyperconjugation preferentially stabilizes many of the endo intermediates and transition structures by 1-5 kcal mol(-1). Our quantum chemical calculations, in conjunction with statistical rate theory models, predict a rate coefficient for the parent CI + SO2 reaction of 3.68 × 10(-11) cm(3) molecule(-1) s(-1), in good agreement with recent experimental measurements. RRKM/master equation simulations based on our quantum chemical data predict a prompt carbonyl + SO3 yield of >95% for the reaction of both the parent and dimethyl CI with SO2. The existence of concerted cycloreversion transition structures 10-15 kcal mol(-1) higher in energy than the HOZ accounts for most of the predicted SO3 formation.

Electron binding energies are evaluated as differences in total energy between the N- and (N ± 1)-electron systems calculated by the nth-order Møller-Plesset perturbation (MPn) theory using the same set of orbitals. The MPn energies up to n = 30 are, in turn, obtained by the determinant-based method of Knowles et al. (Chem. Phys. Lett. 1985, 113, 8-12). The zeroth- through third-order electron binding energies thus determined agree with those obtained by solving the Dyson equation in the diagonal and frequency-independent approximations of the self-energy. However, as n → ∞, they converge at the exact basis-set solutions from the Dyson equation with the exact self-energy, which is nondiagonal and frequency-dependent. This suggests that the MPn energy differences define an alternative diagrammatic expansion of Koopmans-like electron binding energies, which takes into account the perturbation corrections from the off-diagonal elements and frequency dependence of the irreducible self-energy. Our analysis shows that these corrections are included as semireducible and linked-disconnected diagrams, respectively, which are also found in a perturbation expansion of the electron binding energies of the equation-of-motion coupled-cluster methods. The rate of convergence of the electron binding energies with respect to n and its acceleration by Padé approximants are also discussed.