Charge transfer as a mechanism for chlorophyll fluorescence concentration quenching.

Highly concentrated solutions of chlorophyll display rapid fluorescence quenching. The same devastating energy loss is not seen in photosynthetic light-harvesting antenna complexes, despite the need for chromophores to be in close proximity to facilitate energy transfer. A promising, though unconfirmed mechanism for the observed quenching is energy transfer from an excited chlorophyll monomer to a closely associated chlorophyll pair that subsequently undergoes rapid nonradiative decay to the ground state via a short-lived intermediate charge-transfer state. In this work, we make use of newly emerging fast methods in quantum chemistry to assess the feasibility of this proposed mechanism. We calculate rate constants for the initial charge separation, based on Marcus free-energy surfaces extracted from molecular dynamics simulations of solvated chlorophyll pairs, demonstrating that this pathway will compete with fluorescence (i.e., drive quenching) at experimentally measured quenching concentrations. We show that the rate of charge separation is highly sensitive to interchlorophyll distance and the relative orientations of chromophores within a quenching pair. We discuss possible solvent effects on the rate of charge separation (and consequently the degree of quenching), using the light-harvesting complex II (LH2) protein from rps. acidophila as a specific example of how this process might be controlled in a protein environment. Crucially, we reveal that the LH2 antenna protein prevents quenching, even at the high chlorophyll concentrations required for efficient energy transfer, by restricting the range of orientations that neighboring chlorophyll pairs can adopt.

An efficient protocol for excited states of large biochromophores.

Efficient energy transport in photosynthetic antenna is a long-standing source of inspiration for artificial light harvesting materials. However, characterizing the excited states of the constituent chromophores poses a considerable challenge to mainstream quantum chemical and semiempirical excited state methods due to their size and complexity and the accuracy required to describe small but functionally important changes in their properties. In this paper, we explore an alternative approach to calculating the excited states of large biochromophores, exemplified by a specific method for calculating the Qy transition of bacteriochlorophyll a, which we name Chl-xTB. Using a diagonally dominant approximation to the Casida equation and a bespoke parameterization scheme, Chl-xTB can match time-dependent density functional theory's accuracy and semiempirical speed for calculating the potential energy surfaces and absorption spectra of chlorophylls. We demonstrate that Chl-xTB (and other prospective realizations of our protocol) can be integrated into multiscale models, including concurrent excitonic and point-charge embedding frameworks, enabling the analysis of biochromophore networks in a native environment. We exploit this capability to probe the low-frequency spectral densities of excitonic energies and interchromophore interactions in the light harvesting antenna protein LH2 (light harvesting complex 2). The impact of low-frequency protein motion on interchromophore coupling and exciton transport has routinely been ignored due to the prohibitive costs of including it in simulations. Our results provide a more rigorous basis for continued use of this approximation by demonstrating that exciton transition energies are unaffected by low-frequency vibrational coupling to exciton interaction energies.

Informing geometric deep learning with electronic interactions to accelerate quantum chemistry.

Predicting electronic energies, densities, and related chemical properties can facilitate the discovery of novel catalysts, medicines, and battery materials. However, existing machine learning techniques are challenged by the scarcity of training data when exploring unknown chemical spaces. We overcome this barrier by systematically incorporating knowledge of molecular electronic structure into deep learning. By developing a physics-inspired equivariant neural network, we introduce a method to learn molecular representations based on the electronic interactions among atomic orbitals. Our method, OrbNet-Equi, leverages efficient tight-binding simulations and learned mappings to recover high-fidelity physical quantities. OrbNet-Equi accurately models a wide spectrum of target properties while being several orders of magnitude faster than density functional theory. Despite only using training samples collected from readily available small-molecule libraries, OrbNet-Equi outperforms traditional semiempirical and machine learning-based methods on comprehensive downstream benchmarks that encompass diverse main-group chemical processes. Our method also describes interactions in challenging charge-transfer complexes and open-shell systems. We anticipate that the strategy presented here will help to expand opportunities for studies in chemistry and materials science, where the acquisition of experimental or reference training data is costly.

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.

OrbNet Denali: A machine learning potential for biological and organic chemistry with semi-empirical cost and DFT accuracy.

We present OrbNet Denali, a machine learning model for an electronic structure that is designed as a drop-in replacement for ground-state density functional theory (DFT) energy calculations. The model is a message-passing graph neural network that uses symmetry-adapted atomic orbital features from a low-cost quantum calculation to predict the energy of a molecule. OrbNet Denali is trained on a vast dataset of 2.3 × 106 DFT calculations on molecules and geometries. This dataset covers the most common elements in biochemistry and organic chemistry (H, Li, B, C, N, O, F, Na, Mg, Si, P, S, Cl, K, Ca, Br, and I) and charged molecules. OrbNet Denali is demonstrated on several well-established benchmark datasets, and we find that it provides accuracy that is on par with modern DFT methods while offering a speedup of up to three orders of magnitude. For the GMTKN55 benchmark set, OrbNet Denali achieves WTMAD-1 and WTMAD-2 scores of 7.19 and 9.84, on par with modern DFT functionals. For several GMTKN55 subsets, which contain chemical problems that are not present in the training set, OrbNet Denali produces a mean absolute error comparable to those of DFT methods. For the Hutchison conformer benchmark set, OrbNet Denali has a median correlation coefficient of R2 = 0.90 compared to the reference DLPNO-CCSD(T) calculation and R2 = 0.97 compared to the method used to generate the training data (ωB97X-D3/def2-TZVP), exceeding the performance of any other method with a similar cost. Similarly, the model reaches chemical accuracy for non-covalent interactions in the S66x10 dataset. For torsional profiles, OrbNet Denali reproduces the torsion profiles of ωB97X-D3/def2-TZVP with an average mean absolute error of 0.12 kcal/mol for the potential energy surfaces of the diverse fragments in the TorsionNet500 dataset.

Reliable transition properties from excited-state mean-field calculations.

Delta-self-consistent field (ΔSCF) theory is a conceptually simple and computationally inexpensive method for finding excited states. Using the maximum overlap method to guide optimization of the excited state, ΔSCF has been shown to predict excitation energies with a level of accuracy that is competitive with, and sometimes better than, that of time-dependent density functional theory. Here, we benchmark ΔSCF on a larger set of molecules than has previously been considered, and, in particular, we examine the performance of ΔSCF in predicting transition dipole moments, the essential quantity for spectral intensities. A potential downfall for ΔSCF transition dipoles is origin dependence induced by the nonorthogonality of ΔSCF ground and excited states. We propose and test a simple correction for this problem, based on symmetric orthogonalization of the states, and demonstrate its use on bacteriochlorophyll structures sampled from the photosynthetic antenna in purple bacteria.

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.

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.

OrbNet: Deep learning for quantum chemistry using symmetry-adapted atomic-orbital features.

We introduce a machine learning method in which energy solutions from the Schrödinger equation are predicted using symmetry adapted atomic orbital features and a graph neural-network architecture. OrbNet is shown to outperform existing methods in terms of learning efficiency and transferability for the prediction of density functional theory results while employing low-cost features that are obtained from semi-empirical electronic structure calculations. For applications to datasets of drug-like molecules, including QM7b-T, QM9, GDB-13-T, DrugBank, and the conformer benchmark dataset of Folmsbee and Hutchison [Int. J. Quantum Chem. (published online) (2020)], OrbNet predicts energies within chemical accuracy of density functional theory at a computational cost that is 1000-fold or more reduced.

Accurate Hybrid Density Functionals with UW12 Correlation.

In previous work, we suggested a single-parameter hybrid functional containing a novel correlation contribution based on the Unsöld approximation, UW12. This model resembles the explicitly correlated part of MP2-F12 theory and can be written as an explicit formula in terms of the single-particle reduced density matrix. Here, we further investigate hybrid functionals containing UW12 correlation and in particular look at functionals with a large fraction of exact exchange to reduce the self-interaction error. We suggest two new hybrid functionals B-LYP-osUW12 and fB-LYP-osUW12. On the test sets we use, our best hybrid functional overall (B-LYP-osUW12) is of similar accuracy to the best double hybrids considered while eliminating the need for virtual orbitals.

Embedded Mean-Field Theory for Solution-Phase Transition-Metal Polyolefin Catalysis.

Decreasing the wall-clock time of quantum mechanics/molecular mechanics (QM/MM) calculations without sacrificing accuracy is a crucial prerequisite for widespread simulation of solution-phase dynamical processes. In this work, we demonstrate the use of embedded mean-field theory (EMFT) as the QM engine in QM/MM molecular dynamics (MD) simulations to examine polyolefin catalysts in solution. We show that employing EMFT in this mode preserves the accuracy of hybrid-functional DFT in the QM region, while providing up to 20-fold reductions in the cost per SCF cycle, thereby increasing the accessible simulation time-scales. We find that EMFT reproduces DFT-computed binding energies and optimized bond lengths to within chemical accuracy, as well as consistently ranking conformer stability. Furthermore, solution-phase EMFT/MM simulations provide insight into the interaction strength of strongly coordinating and bulky counterions.

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.

Structure and Efficiency in Bacterial Photosynthetic Light Harvesting.

Photosynthetic organisms use networks of chromophores to absorb and deliver solar energy to reaction centers. We present a detailed model of the light-harvesting complexes in purple bacteria, including explicit interaction with sunlight, radiative and nonradiative energy loss, and dephasing and thermalizing effects of coupling to a vibrational bath. We capture the effect of slow vibrations by introducing time-dependent disorder. Our model describes the experimentally observed high efficiency of light harvesting, despite the absence of long-range quantum coherence. The one-exciton part of the quantum state fluctuates continuously but remains highly mixed at all times. These results suggest a relatively minor role for structure in determining efficiency. We build hypothetical models with randomly arranged chromophores but still observe high efficiency when nearest-neighbor distances are comparable to those in nature. This helps explain the high transport efficiency in organisms with widely differing antenna structures and suggests new design criteria for artificial light-harvesting devices.

Projection-Based Wavefunction-in-DFT Embedding.

Complex chemical systems present challenges to electronic structure theory stemming from large system sizes, subtle interactions, coupled dynamical time scales, and electronically nonadiabatic effects. New methods are needed to perform reliable, rigorous, and affordable electronic structure calculations for simulating the properties and dynamics of such systems. This Account reviews projection-based quantum embedding for electronic structure, which provides a formally exact method for density functional theory (DFT) embedding. The method also provides a rigorous and accurate approach for describing a small part of a chemical system at the level of a correlated wavefunction (WF) method while the remainder of the system is described at the level of DFT. A key advantage of projection-based embedding is that it can be formulated in terms of an extremely simple level-shift projection operator, which eliminates the need for any optimized effective potential calculation or kinetic energy functional approximation while simultaneously ensuring that no extra programming is needed to perform WF-in-DFT embedding with an arbitrary WF method. The current work presents the theoretical underpinnings of projection-based embedding, describes use of the method for combining wavefunction and density functional theories, and discusses technical refinements that have improved the applicability and robustness of the method. Applications of projection-based WF-in-DFT embedding are also reviewed, with particular focus on recent work on transition-metal catalysis, enzyme reactivity, and battery electrolyte decomposition. In particular, we review the application of projection-based embedding for the prediction of electrochemical potentials and reaction pathways in a Co-centered hydrogen evolution catalyst. Projection-based WF-in-DFT calculations are shown to provide quantitative accuracy while greatly reducing the computational cost compared with a reference coupled cluster calculation on the full system. Additionally, projection-based WF-in-DFT embedding is used to study the mechanism of citrate synthase; it is shown that projection-based WF-in-DFT largely eliminates the sensitivity of the potential energy landscape to the employed DFT exchange-correlation functional. Finally, we demonstrate the use of projection-based WF-in-DFT to study electron transfer reactions associated with battery electrolyte decomposition. Projection-based WF-in-DFT embedding is used to calculate the oxidation potentials of neat ethylene carbonate (EC), neat dimethyl carbonate (DMC), and 1:1 mixtures of EC and DMC in order to overcome qualitative inaccuracies in the electron densities and ionization energies obtained from conventional DFT methods. By further embedding the WF-in-DFT description in a molecular mechanics point-charge environment, this work enables an explicit description of the solvent and ensemble averaging of the solvent configurations. Looking forward, we anticipate continued refinement of the projection-based embedding methodology as well as its increasingly widespread application in diverse areas of chemistry, biology, and materials science.

Imaging covalent bond formation by H atom scattering from graphene.

Viewing the atomic-scale motion and energy dissipation pathways involved in forming a covalent bond is a longstanding challenge for chemistry. We performed scattering experiments of H atoms from graphene and observed a bimodal translational energy loss distribution. Using accurate first-principles dynamics simulations, we show that the quasi-elastic channel involves scattering through the physisorption well where collision sites are near the centers of the six-membered C-rings. The second channel results from transient C-H bond formation, where H atoms lose 1 to 2 electron volts of energy within a 10-femtosecond interaction time. This remarkably rapid form of intramolecular vibrational relaxation results from the C atom's rehybridization during bond formation and is responsible for an unexpectedly high sticking probability of H on graphene.

Projector-Based Embedding Eliminates Density Functional Dependence for QM/MM Calculations of Reactions in Enzymes and Solution.

Combined quantum mechanics/molecular mechanics (QM/MM) methods are increasingly widely utilized in studies of reactions in enzymes and other large systems. Here, we apply a range of QM/MM methods to investigate the Claisen rearrangement of chorismate to prephenate, in solution, and in the enzyme chorismate mutase. Using projector-based embedding in a QM/MM framework, we apply treatments up to the CCSD(T) level. We test a range of density functional QM/MM methods and QM region sizes. The results show that the calculated reaction energetics are significantly more sensitive to the choice of density functional than they are to the size of the QM region in these systems. Projector-based embedding of a wave function method in DFT reduced the 13 kcal/mol spread in barrier heights calculated at the DFT/MM level to a spread of just 0.3 kcal/mol, essentially eliminating dependence on the functional. Projector-based embedding of correlated ab initio methods provides a practical method for achieving high accuracy for energy profiles derived from DFT and DFT/MM calculations for reactions in condensed phases.

Even-handed subsystem selection in projection-based embedding.

Projection-based embedding offers a simple framework for embedding correlated wavefunction methods in density functional theory. Partitioning between the correlated wavefunction and density functional subsystems is performed in the space of localized molecular orbitals. However, during a large geometry change-such as a chemical reaction-the nature of these localized molecular orbitals, as well as their partitioning into the two subsystems, can change dramatically. This can lead to unphysical cusps and even discontinuities in the potential energy surface. In this work, we present an even-handed framework for localized orbital partitioning that ensures consistent subsystems across a set of molecular geometries. We illustrate this problem and the even-handed solution with a simple example of an SN2 reaction. Applications to a nitrogen umbrella flip in a cobalt-based CO2 reduction catalyst and to the binding of CO to Cu clusters are presented. In both cases, we find that even-handed partitioning enables chemically accurate embedding with modestly sized embedded regions for systems in which previous partitioning strategies are problematic.

Wavefunction-like Correlation Model for Use in Hybrid Density Functionals.

We present Unsöld-W12 (UW12), an approximation to the correlation energy of molecules that is an explicit functional of the single-particle reduced-density matrix. The approximation resembles one part of modern explicitly correlated second-order Møller-Plesset (MP2) theory and is intended as an alternative to MP2 in double-hybrid exchange-correlation functionals. Orbital optimization with UW12 is straightforward, and the UW12 energy is evaluated without a double summation over unoccupied orbitals, leading to a faster basis-set convergence than is seen in double-hybrid functionals. We suggest a one-parameter hybrid exchange-correlation functional XCH-BLYP-UW12. XCH-BLYP-UW12 is similar to double-hybrid functionals, but contains UW12 correlation instead of MP2 correlation. We find that XCH-BLYP-UW12 is more accurate than the existing double-hybrid functional B2-PLYP for small-molecule main-group reaction barrier heights and has roughly the same accuracy as the existing hybrid functional B3LYP for atomization energies.

Multiscale analysis of enantioselectivity in enzyme-catalysed 'lethal synthesis' using projector-based embedding.

The action of fluoroacetate as a broad-spectrum mammalian pesticide depends on the 'lethal synthesis' of fluorocitrate by citrate synthase, through a subtle enantioselective enolization of fluoroacetyl-coenzyme A. In this work, we demonstrate how a projection-based embedding method can be applied to calculate coupled cluster (CCSD(T)) reaction profiles from quantum mechanics/molecular mechanics optimized pathways for this enzyme reaction. Comparison of pro-R and pro-S proton abstraction in citrate synthase at the CCSD(T)-in-DFT//MM level yields the correct enantioselectivity. We thus demonstrate the potential of projection-based embedding for determining stereoselectivity in enzymatic systems. We further show that the method is simple to apply, eliminates variability due to the choice of density functional theory functional and allows the efficient calculation of CCSD(T) quality enzyme reaction barriers.

Pushing the Limits of EOM-CCSD with Projector-Based Embedding for Excitation Energies.

The calculation of accurate excitation energies using ab initio electronic structure methods such as standard equation of motion coupled cluster singles and doubles (EOM-CCSD) has been cost prohibitive for large systems. In this work, we use a simple projector-based embedding scheme to calculate the EOM-CCSD excitation energies of acrolein solvated in water molecules modeled using density functional theory (DFT). We demonstrate the accuracy of this approach gives excitation energies within 0.01 eV of full EOM-CCSD, but with significantly reduced computational cost. This approach is also shown to be relatively invariant to the choice of functional used in the environment and allows for the description of systems with large numbers of basis functions (>1000) to be treated using state-of-the-art wave function methods. The flexibility of embedding to select orbitals to add to the excited-state method provides insights into the origins of the excitations and can reduce artifacts that could arise in traditional linear response time-dependent DFT (LR-TDDFT).