A density-fitting implementation of the density-based basis-set correction method.

This work reports an efficient density-fitting implementation of the density-based basis-set correction (DBBSC) method in the MOLPRO software. This method consists in correcting the energy calculated by a wave-function method with a given basis set by an adapted basis-set correction density functional incorporating the short-range electron correlation effects missing in the basis set, resulting in an accelerated convergence to the complete-basis-set limit. Different basis-set correction density-functional approximations are explored and the complementary-auxiliary-basis-set single-excitation correction is added. The method is tested on a benchmark set of reaction energies at the second-order Møller-Plesset (MP2) level and a comparison with the explicitly correlated MP2-F12 method is provided. The results show that the DBBSC method greatly accelerates the basis convergence of MP2 reaction energies, without reaching the accuracy of the MP2-F12 method but with a lower computational cost.

Perturbation-adapted perturbation theory.

A new general approach is introduced for defining an optimum zero-order Hamiltonian for Rayleigh-Schrödinger perturbation theory. Instead of taking the operator directly from a model problem, it is constructed to be a best fit to the exact Hamiltonian within any desired functional form. When applied to many-body perturbation theory for electrons, strongly improved convergence is observed in cases where the conventional Fock Hamiltonian leads to divergence or slow convergence.

Thermochemical evaluation of adaptive and fixed density functional theory quadrature schemes.

A systematic study is made of the accuracy and efficiency of a number of existing quadrature schemes for molecular Kohn-Sham Density-Functional Theory (DFT) using 408 molecules and 254 chemical reactions. Included are the fixed SG-x (x = 0-3) grids of Gill et al., Dasgupta, and Herbert, the 3-zone grids of Treutler and Ahlrichs, a fixed five-zone grid implemented in Molpro, and a new adaptive grid scheme. While all methods provide a systematic reduction of errors upon extension of the grid sizes, significant differences are observed in the accuracies for similar grid sizes with various approaches. For the tests in this work, the SG-x fixed grids are less suitable to achieve high accuracies in the DFT integration, while our new adaptive grid performed best among the schemes studied in this work. The extra computational time to generate the adaptive grid scales linearly with molecular size and is negligible compared with the time needed for the self-consistent field iterations for large molecules. A comparison of the grid accuracies using various density functionals shows that meta-GGA functionals need larger integration grids than GGA functionals to reach the same degree of accuracy, confirming previous investigations of the numerical stability of meta-GGA functionals. On the other hand, the grid integration errors are almost independent of the basis set, and the basis set errors are mostly much larger than the errors caused by the numerical integrations, even when using the smallest grids tested in this work.

Polaritonic effects in the vibronic spectrum of molecules in an optical cavity.

We present a new computational framework to describe polaritons, which treats photons and electrons on the same footing using coupled-cluster theory. As a proof of concept, we study the coupling between the first electronically excited state of carbon monoxide and an optical cavity. In particular, we focus on how the interaction with the photonic mode changes the vibrational spectroscopic signature of the electronic state and how this is affected when tuning the cavity frequency and the light-matter coupling strength. For this purpose, we consider different methodologies and investigate the validity of the Born-Oppenheimer approximation in such situations.

Molecular second-quantized Hamiltonian: Electron correlation and non-adiabatic coupling treated on an equal footing.

We introduce a new theoretical and computational framework for treating molecular quantum mechanics without the Born-Oppenheimer approximation. The molecular wavefunction is represented in a tensor-product space of electronic and vibrational basis functions, with electronic basis chosen to reproduce the mean-field electronic structure at all geometries. We show how to transform the Hamiltonian to a fully second-quantized form with creation/annihilation operators for electronic and vibrational quantum particles, paving the way for polynomial-scaling approximations to the tensor-product space formalism. In addition, we make a proof-of-principle application of the new Ansatz to the vibronic spectrum of C2.

Coupling electrons and vibrations in molecular quantum chemistry.

We derive an electron-vibration model Hamiltonian in a quantum chemical framework and explore the extent to which such a Hamiltonian can capture key effects of nonadiabatic dynamics. The model Hamiltonian is a simple two-body operator, and we make preliminary steps at applying standard quantum chemical methods to evaluate its properties, including mean-field theory, linear response, and a primitive correlated model. The Hamiltonian can be compared to standard vibronic Hamiltonians, but it is constructed without reference to potential energy surfaces through direct differentiation of the one- and two-electron integrals at a single reference geometry. The nature of the model Hamiltonian in the harmonic and linear-coupling regime is investigated for pyrazine, where a simple time-dependent calculation including electron-vibration correlation is demonstrated to exhibit the well-studied population transfer between the S2 and S1 excited states.

MCSCF optimization revisited. II. Combined first- and second-order orbital optimization for large molecules.

A new orbital optimization for the multiconfiguration self-consistent field method is presented. This method combines a second-order (SO) algorithm for the optimization of the active orbitals with the first-order super configuration interaction (SCI) optimization of the remaining closed-virtual rotations and is denoted as the SO-SCI method. The SO-SCI method significantly improves the convergence as compared to the conventional SCI method. In combination with density fitting, the intermediates from the gradient calculation can be reused to evaluate the two-electron integrals required for the active Hessian without introducing a large computational overhead. The orbitals and CI coefficients are optimized alternately, but the CI-orbital coupling is accounted for by the limited memory Broyden-Fletcher-Goldfarb-Shanno quasi-Newton method. This further improves the speed of convergence. The method is applicable to large molecules. The efficiency and robustness of the presented method is demonstrated in benchmark calculations for 21 aromatic molecules as well as for various transition metal complexes with up to 826 electrons and 5154 basis functions.

The Molpro quantum chemistry package.

Molpro is a general purpose quantum chemistry software package with a long development history. It was originally focused on accurate wavefunction calculations for small molecules but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding, and anharmonic vibrational spectra. In addition to conventional input-file specification of calculations, Molpro calculations can now be specified and analyzed via a new graphical user interface and through a Python framework.

An Extended Computational Study of Criegee Intermediate-Alcohol Reactions.

High-level ab initio calculations (DF-LCCSD(T)-F12a//B3LYP/aug-cc-pVTZ) are performed on a range of stabilized Criegee intermediate (sCI)-alcohol reactions, computing reaction coordinate energies, leading to the formation of α-alkoxyalkyl hydroperoxides (AAAHs). These potential energy surfaces are used to model bimolecular reaction kinetics over a range of temperatures. The calculations performed in this work reproduce the complicated temperature-dependent reaction rates of CH2OO and (CH3)2COO with methanol, which have previously been experimentally determined. This methodology is then extended to compute reaction rates of 22 different Criegee intermediates with methanol, including several intermediates derived from isoprene ozonolysis. In some cases, sCI-alcohol reaction rates approach those of sCI-(H2O)2. This suggests that in regions with elevated alcohol concentrations, such as urban Brazil, these reactions may generate significant quantities of AAAHs and may begin to compete with sCI reactions with other trace tropospheric pollutants such as SO2. This work also demonstrates the ability of alcohols to catalyze the 1,4-H transfer unimolecular decomposition of α-methyl substituted sCIs.

Second-order MCSCF optimization revisited. I. Improved algorithms for fast and robust second-order CASSCF convergence.

A new improved implementation of the second-order multiconfiguration self-consistent field optimization method of Werner and Knowles [J. Chem. Phys. 82, 5053 (1985)] is presented. It differs from the original method by more stable and efficient algorithms for minimizing the second-order energy approximation in the so-called microiterations. Conventionally, this proceeds by alternating optimizations of the orbitals and configuration (CI) coefficients and is linearly convergent. The most difficult part is the orbital optimization, which requires solving a system of nonlinear equations that are often strongly coupled. We present a much improved algorithm for solving this problem, using an iterative subspace method that includes part of the orbital Hessian explicitly, and discuss different strategies for performing the uncoupled optimization in a most efficient manner. Second, we present a new solver in which the orbital-CI coupling is treated explicitly. This leads to quadratic convergence of the microiterations but requires many additional evaluations of reduced (transition) density matrices. In difficult optimization problems with a strong coupling of the orbitals and CI coefficients, it leads to much improved convergence of both the macroiterations and the microiterations. Third, the orbital-CI coupling is treated approximately using a quasi-Newton approach with Broyden-Fletcher-Goldfarb-Shanno updates of the orbital Hessian. It is demonstrated that this converges almost as well as the explicitly coupled method but avoids the additional effort for computing many transition density matrices. The performance of the three methods is compared for a set of 21 aromatic molecules, an Fe(ii)-porphine transition metal complex, as well as for the [Cu2O2(NH3) 6]2+, FeCl3, Co2(CO)6C2H2, and Al4O2 complexes. In all cases, faster and more stable convergence than with the original implementation is achieved.

Direct quantum dynamics using variational Gaussian wavepackets and Gaussian process regression.

The method of direct variational quantum nuclear dynamics in a basis of Gaussian wavepackets, combined with the potential energy surfaces fitted on-the-fly using Gaussian process regression, is described together with its implementation. Enabling exact and efficient analytic evaluation of Hamiltonian matrix elements, this approach allows for black-box quantum dynamics of multidimensional anharmonic molecular systems. Example calculations of intra-molecular proton transfer on the electronic ground state of salicylaldimine are provided, and future algorithmic improvements as well as the potential for multiple-state non-adiabatic dynamics are discussed.

Oxygen Activation Switch in the Copper Amine Oxidase of Escherichia coli.

Copper amine oxidases (CuAOs) are metalloenzymes that reduce molecular oxygen to hydrogen peroxide during catalytic turnover of primary amines. In addition to Cu2+ in the active site, two peripheral calcium sites, ∼32 Šfrom the active site, have roles in Escherichia coli amine oxidase (ECAO). The buried Ca2+ (Asp533, Leu534, Asp535, Asp678, and Ala679) is essential for full-length protein production, while the surface Ca2+ (Glu573, Tyr667, Asp670, and Glu672) modulates biogenesis of the 2,4,5-trihydroxyphenylalanine quinone (TPQ) cofactor. The E573Q mutation at the surface site prevents calcium binding and TPQ biogenesis. However, TPQ biogenesis can be restored by a suppressor mutation (I342F) in the proposed oxygen delivery channel to the active site. While supporting TPQ biogenesis (∼60% WTECAO TPQ), I342F/E573Q has almost no amine oxidase activity (∼4.6% WTECAO activity). To understand how these long-range mutations have major effects on TPQ biogenesis and catalysis, we employed ultraviolet-visible spectroscopy, steady-state kinetics, inhibition assays, and X-ray crystallography. We show that the surface metal site controls the equilibrium (disproportionation) of the Cu2+-substrate reduced TPQ (TPQAMQ) Cu+-TPQ semiquinone (TPQSQ) couple. Removal of the calcium ion from this site by chelation or mutagenesis shifts the equilibrium to Cu2+-TPQAMQ or destabilizes Cu+-TPQSQ. Crystal structure analysis shows that TPQ biogenesis is stalled at deprotonation in the Cu2+-tyrosinate state. Our findings support WTECAO using the inner sphere electron transfer mechanism for oxygen reduction during catalysis, and while a Cu+-tyrosyl radical intermediate is not essential for TPQ biogenesis, it is required for efficient biogenesis.

Dermal Absorption of Pesticide Residues.

Current guidance for dermal exposure assessment of plant protection products typically uses in vitro skin penetration data for the active ingredient when applied as both the concentrated product and relevant spray dilutions thereof. However, typical re-entry scenarios involve potential skin exposure to a "dried residue" of the spray dilution, from which the absorption of a pesticide may be quite different. The research reported in this paper has shown: (1) The method to assess the transfer of dried pesticide residues from a surface to the skin is reproducible for four active ingredients of diverse physicochemical properties, after their application in commercially relevant formulations. (2) Skin absorption of all four pesticides examined was significantly less from a dried residue than from a spray dilution; the difference, in general, was of the order of a factor of 2. (3) Decontamination experiments with one of the active ingredients tested (trinexapac-ethyl) showed that, post-exposure to a spray dilution, skin surface cleaning must be performed within 1 h to significantly reduce potential systemic exposure (relative to continual contact for 24 h); in contrast, after contact with a dried residue, the sooner decontamination was performed, the greater the decrease in exposure achieved, even when the time of contact was as long as 8 h.

Quasi-variational coupled-cluster theory: Performance of perturbative treatments of connected triple excitations.

Quasi-variational coupled-cluster methods are applied to a selection of diatomic molecules. The potential energy curves, spectroscopic constants, and size consistency errors are calculated and compared to those obtained from both single- and multi-reference methods. The effects of connected triple excitations are introduced with either the standard perturbative (T) formulation, or in the renormalised form, and its symmetrised approximation. It is found that the renormalised ansatz is significantly superior to the standard formulation when describing bond breaking and that in most circumstances, the computationally simpler symmetrisation gives nearly identical results.

One-particle many-body Green's function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms.

A thorough analytical and numerical characterization of the whole perturbation series of one-particle many-body Green's function (MBGF) theory is presented in a pedagogical manner. Three distinct but equivalent algebraic (first-quantized) recursive definitions of the perturbation series of the Green's function are derived, which can be combined with the well-known recursion for the self-energy. Six general-order algorithms of MBGF are developed, each implementing one of the three recursions, the ΔMPn method (where n is the perturbation order) [S. Hirata et al., J. Chem. Theory Comput. 11, 1595 (2015)], the automatic generation and interpretation of diagrams, or the numerical differentiation of the exact Green's function with a perturbation-scaled Hamiltonian. They all display the identical, nondivergent perturbation series except ΔMPn, which agrees with MBGF in the diagonal and frequency-independent approximations at 1≤n≤3 but converges at the full-configuration-interaction (FCI) limit at n=∞ (unless it diverges). Numerical data of the perturbation series are presented for Koopmans and non-Koopmans states to quantify the rate of convergence towards the FCI limit and the impact of the diagonal, frequency-independent, or ΔMPn approximation. The diagrammatic linkedness and thus size-consistency of the one-particle Green's function and self-energy are demonstrated at any perturbation order on the basis of the algebraic recursions in an entirely time-independent (frequency-domain) framework. The trimming of external lines in a one-particle Green's function to expose a self-energy diagram and the removal of reducible diagrams are also justified mathematically using the factorization theorem of Frantz and Mills. Equivalence of ΔMPn and MBGF in the diagonal and frequency-independent approximations at 1≤n≤3 is algebraically proven, also ascribing the differences at n = 4 to the so-called semi-reducible and linked-disconnected diagrams.

Probing the molecular mechanisms in copper amine oxidases by generating heterodimers.

For some homodimeric copper amine oxidases (CuAO), there is suggestive evidence of differential activity at the two active sites implying potential cooperativity between the two monomers. To examine this phenomenon for the Arthrobacter globiformis CuAO (AGAO), we purified a heterodimeric form of the enzyme for comparison with the homodimer. The heterodimer comprises an active wild-type monomer and an inactive monomer in which an active-site tyrosine is mutated to phenylalanine (Y382F). This mutation prevents the formation of the trihydroxyphenylalanine quinone (TPQ) cofactor. A pETDuet vector and a dual fusion tag strategy was used to purify heterodimers (WT/Y382F) from homodimers. Purity was confirmed by western blot and native PAGE analyses. Spectral and kinetic studies support the view that whether there are one or two functional monomers in the dimer, the properties of each functional monomer are the same, thus indicating no communication between the active sites in this bacterial enzyme.

In Vitro Method to Quantify Dermal Absorption of Pesticide Residues.

All pesticides must go through a rigorous risk assessment process in order to show that they are safe for use.With respect to dermal risk assessment for re-entry workers, the absorption value applied to predict systemic dose from this external exposure is obtained by testing liquid forms of the pesticide in vivo and/or in vitro. However, in a real exposure scenario, the worker would be exposed to a dried residue, for which little or no absorption data are available. This study has developed a novel methodology for assessing the dermal absorption of pesticides from dried residues and aims ultimately to use this methodology to obtain more realistic absorption values for the risk assessment.

Analytic nuclear forces and molecular properties from full configuration interaction quantum Monte Carlo.

Unbiased stochastic sampling of the one- and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, "replica" ensemble of walkers, whose population evolves in imaginary time independently from the first and which entails only modest additional computational overheads. The matrices obtained from this approach are shown to be representative of full configuration-interaction quality and hence provide a realistic opportunity to achieve high-quality results for a range of properties whose operators do not necessarily commute with the Hamiltonian. A density-matrix formulated quasi-variational energy estimator having been already proposed and investigated, the present work extends the scope of the theory to take in studies of analytic nuclear forces, molecular dipole moments, and polarisabilities, with extensive comparison to exact results where possible. These new results confirm the suitability of the sampling technique and, where sufficiently large basis sets are available, achieve close agreement with experimental values, expanding the scope of the method to new areas of investigation.

Rigorously extensive orbital-invariant renormalized perturbative triples corrections from quasi-variational coupled cluster theory.

We show that, by making use of the linked tensor objects inherent to the approach, Orbital-optimised Quasi-Variational Coupled Cluster Theory (OQVCCD) leads naturally to a computationally-trivial, rigorously extensive, and orbital-invariant renormalization of the standard (T) correction for the perturbative inclusion of the effects of connected triple excitations. The resulting prototype method, renormalized perturbative triple OQVCCD (R-OQVCCD(T)), is demonstrated to predict potential energy curves for single bond-breaking processes of significantly higher accuracy than OQVCCD with the standard perturbative triple-excitation correction (OQVCCD(T)) itself, and to be in good numerical correspondence with the existing renormalized (R-CCSD(T)) and completely renormalized (CR-CCSD(T)) coupled-cluster singles doubles triples methods, while continuing to provide descriptions of multiple bond-breaking processes of OQVCCD(T) quality.