Molecular π-Orbital Construction for Non-Planar Conjugated Systems.

We extend the π-orbital space (PiOS) method introduced for planar π-conjugated molecular systems [J. Chem. Theory Comput. 2019, 15, 1679] to also allow constructing efficient π-orbital active spaces for non-planar π-conjugated systems. We demonstrate the performance of this method with multiconfigurational and multireference calculations on prototypical non-planar π-systems: cycloacenes, short carbon nanotubes, various conformations of the 2,2-bipyridine anion, and C20 fullerenes.

Structural and Thermodynamic Effects on the Kinetics of C-H Oxidation by Multisite Proton-Coupled Electron Transfer in Fluorenyl Benzoates.

Our recent experimental and theoretical investigations have shown that fluorene C-H bonds can be activated through a mechanism in which the proton and electron are transferred from the C-H bond to a separate base and oxidant in a concerted, elementary step. This multisite proton-coupled electron transfer (MS-PCET) mechanism for C-H bond activation was shown to be facilitated by shorter proton donor-acceptor distances. With the goal of intentionally modulating this donor-acceptor distance, we have now studied C-H MS-PCET in the 3-methyl-substituted fluorenyl benzoate (2-Flr-3-Me-BzO-). This derivative was readily oxidized by ferrocenium oxidants by initial C-H MS-PCET, with rate constants that were 6-21 times larger than those for 2-Flr-BzO- with the same oxidants. Structural comparisons by X-ray crystallography and by computations showed that addition of the 3-methyl group caused the expected steric compression; however, the relevant C···O- proton donor-acceptor distance was longer, due to a twist of the carboxylate group. The structural changes induced by the 3-Me group increased the basicity of the carboxylate, weakened the C-H bond, and reduced the reorganization energy for C-H bond cleavage. Thus, the rate enhancement for 2-Flr-3-Me-BzO- was due to effects on the thermochemistry and kinetic barrier, rather than from compression of the C···O- proton donor-acceptor distance. These results highlight both the challenges of controlling molecules on the 0.1 Å length scale and the variety of parameters that affect PCET rate constants.

Glutamate Mediates Proton-Coupled Electron Transfer Between Tyrosines 730 and 731 in Escherichia coli Ribonucleotide Reductase.

Ribonucleotide reductase (RNR) is an essential enzyme in DNA synthesis for all living organisms. It reduces ribonucleotides to the corresponding deoxyribonucleotides by a reversible radical transfer mechanism. The active form of E. coli Ia RNR is composed of two subunits, α and ß, which form an active asymmetric α2ß2 complex. The radical transfer pathway involves a series of proton-coupled electron transfer (PCET) reactions spanning α and ß over ∼32 Å. Herein, quantum mechanical/molecular mechanical free energy simulations of PCET between tyrosine residues Y730 and Y731 are performed on the recently solved cryo-EM structure of the active α2ß2 complex, which includes a pre-turnover α/ß pair with an ordered PCET pathway and a post-turnover α'/ß' pair. The free energy surfaces in both the pre- and post-turnover states are computed. According to the simulations, forward radical transfer from Y731 to Y730 is thermodynamically favored in the pre-turnover state, and backward radical transfer is favored in the post-turnover state, consistent with the reversible mechanism. E623, a glutamate residue that is near these tyrosines only in the pre-turnover state, is discovered to play a key role in facilitating forward radical transfer by thermodynamically stabilizing the radical on Y730 through hydrogen-bonding and electrostatic interactions and lowering the free energy barrier via a proton relay mechanism. Introduction of fluorinated Y731 exhibits expected thermodynamic trends without altering the basic mechanism. These simulations suggest that E623 influences the directionality of PCET between Y731 and Y730 and predict that mutation of E623 will impact catalysis.

Excited State Molecular Dynamics of Photoinduced Proton-Coupled Electron Transfer in Anthracene-Phenol-Pyridine Triads.

Photoinduced proton-coupled electron transfer (PCET) in anthracene-phenol-pyridine triads exhibits inverted region behavior, where the more thermodynamically favorable process is slower. The long-lived transient charge-separated state (CSS) associated with electron transfer from phenol to anthracene and inverted region behavior were only observed experimentally for certain triads. Herein, excited state molecular dynamics simulations were performed on four different triads to simulate the nonequilibrium dynamics following photoexcitation to the locally excited state (LES) of anthracene. These simulations identified two distinct PCET pathways: the triads exhibiting inverted region behavior transitioned from the LES to the CSS, whereas the other triads transitioned to a local electron-proton transfer (LEPT) state within phenol and pyridine. The simulations suggest that PCET to the LEPT state is slower than PCET to the CSS and provides an alternative relaxation pathway. The mechanistic pathways, as well as the time scales of the electron and proton transfers, can be controlled by tuning the substituents.

Recent developments in the PySCF program package.

PySCF is a Python-based general-purpose electronic structure platform that supports first-principles simulations of molecules and solids as well as accelerates the development of new methodology and complex computational workflows. This 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.

Substituent Effects on Photochemistry of Anthracene-Phenol-Pyridine Triads Revealed by Multireference Calculations.

Inverted region behavior for concerted proton-coupled electron transfer (PCET) was recently demonstrated for biomimetic anthracene-phenol-pyridine molecular triads. Photoexcitation of the anthracene to a locally excited state (LES) is followed by concerted electron transfer from the phenol to the anthracene and proton transfer from the phenol to the pyridine, forming a relatively long-lived charge separated state (CSS). The long-lived CSS and the inverted region behavior associated with the decay from the CSS to the ground state through charge recombination were experimentally observed only for triads with certain substituents on the anthracene and the pyridine. To explain this distinction, we computed the proton potential energy curves in four substituted triads using the complete active space self-consistent-field method and multireference perturbation theory, including solvent effects with a dielectric continuum model. The calculations revealed a local electron-proton transfer (LEPT) state, in which both the electron and proton transfer from the phenol to the pyridine. When the LEPT state is lower in energy than the CSS, it may provide an alternative pathway for fast decay from the LES to the ground state and thereby preclude detection of the CSS and the inverted region behavior. These calculations predict that substituents stabilizing negative charge on the pyridine and destabilizing negative charge on the anthracene will favor the LEPT pathway, while substituents with the reverse effects will favor the CSS pathway, which could exhibit inverted region behavior. These insights about the stabilization of energy-storing charge-separated states have implications for designing and controlling PCET reactions in artificial photosynthetic systems and other energy conversion processes.

Strategies for Enhancing the Rate Constant of C-H Bond Cleavage by Concerted Proton-Coupled Electron Transfer.

Recently selective C-H bond cleavage under mild conditions with weak oxidants was reported for fluorenyl-benzoates. This mechanism is based on multi-site concerted proton-coupled electron transfer (PCET) involving intermolecular electron transfer to an outer-sphere oxidant coupled to intramolecular proton transfer to a well-positioned proton acceptor. The electron transfer driving force depends predominantly on the oxidant, and the proton transfer driving force depends mainly on the basicity of the carboxylate, which is influenced by the substituent on the benzoate fragment. Experiments showed that the rate constants are much more sensitive to the carboxylate basicity than to the redox potential of the oxidant. Herein a vibronically nonadiabatic PCET theory is used to explain how changing the driving force for the electron and proton transfer components of the reaction through varying the oxidant and the substituent, respectively, impacts the PCET rate constant. In addition to increasing the driving force for proton transfer, enhancing the basicity of the carboxylate also decreases the equilibrium proton donor-acceptor distance, thereby facilitating the sampling of shorter proton donor-acceptor distances. This additional effect arising from the strong dependence of proton transfer on the proton donor-acceptor distance provides an explanation for the greater sensitivity of the rate constant to the carboxylate basicity than to the redox potential of the oxidant. These fundamental insights have broad implications for developing new strategies to activate C-H bonds, specifically by designing systems with shorter equilibrium proton donor-acceptor distances.

Constructing Molecular π-Orbital Active Spaces for Multireference Calculations of Conjugated Systems.

Molecules with conjugated π systems often feature strong electron correlation and therefore require multireference methods for a reliable computational description. A key prerequisite for the successful application of such methods is the choice of a suitable active space. Herein the automated π-orbital space (PiOS) method for selecting active spaces for multireference calculations of conjugated π systems is presented. This approach allows the construction of small but effective active spaces based on Hückel theory. To demonstrate its performance, π → π* excitations for benzene, octatetraene, and free-base porphine are computed. In addition, this technique can be combined with the automated atomic valence active space method to compute excitations in complex systems with multiple conjugated fragments. This combined approach was used to generate two-dimensional potential energy surfaces for multiple electronic states associated with photoinduced electron-coupled double proton transfer in the blue-light-using flavin photoreceptor protein. These types of methods for the automated selection of active space orbitals are important for ensuring consistency and reproducibility of multireference approaches for a wide range of chemical and biological systems.

Electron-Coupled Double Proton Transfer in the Slr1694 BLUF Photoreceptor: A Multireference Electronic Structure Study.

Photoreceptor proteins control vital cellular responses to light. The photocycle of the Slr1694 blue light using flavin photoreceptor is initiated by photoexcitation to a locally excited state within the flavin, followed by electron transfer from Tyr8 to the flavin and a proton relay from Tyr8 to the flavin via an intervening glutamine. Herein, the two-dimensional excited state potential energy surfaces associated with this double proton-transfer reaction are computed using the complete active space self-consistent-field method and multiconfigurational perturbation theory, including the protein and solvent environment with electrostatic embedding. The double proton-transfer reaction was found to be energetically unfavorable in the ground state and locally excited state but energetically favorable in the charge-transfer state corresponding to electron transfer from Tyr8 to the flavin. These results indicate that the proton-coupled electron transfer process is sequential, with electron transfer preceding double proton transfer, and that the double proton-transfer reaction is also sequential, with proton transfer from Tyr8 to Gln50 followed by proton transfer from Gln50 to the flavin. The barrier is lower for the first proton-transfer reaction, and both barriers are significantly influenced by geometrical changes within the active site, particularly the proton donor-acceptor distance as well as the protein environment. These calculations provide insight into the impact of protein reorganization and electrostatics on the excited electronic states prior to and during the double proton-transfer reaction. This interplay between excited states and the environment has implications for other photoreceptor proteins.

Theoretical Study of C-H Bond Cleavage via Concerted Proton-Coupled Electron Transfer in Fluorenyl-Benzoates.

Developing new strategies to activate and cleave C-H bonds is important for a broad range of applications. Recently a new approach for C-H bond activation using multi-site concerted proton-coupled electron transfer (PCET) involving intermolecular electron transfer to an oxidant coupled to intramolecular proton transfer was reported. For a series of oxidants reacting with 2-(9 H-fluoren-9-yl)benzoate, experimental studies revealed an atypical Brønsted α, defined as the slope of the logarithm of the PCET rate constant versus the logarithm of the equilibrium constant or the scaled driving force. Herein this reaction is modeled with a vibronically nonadiabatic PCET theory. Hydrogen tunneling, thermal sampling of the proton donor-acceptor mode, solute and solvent reorganization, and contributions from excited vibronic states are found to play important roles. The calculations qualitatively reproduce the experimental observation of a Brønsted α significantly less than 0.5 and explain this shallow slope in terms of exoergic processes between pairs of electron-proton vibronic states. These fundamental mechanistic insights may guide the design of more effective strategies for C-H bond activation and cleavage.

Electron paramagnetic resonance g-tensors from state interaction spin-orbit coupling density matrix renormalization group.

We present a state interaction spin-orbit coupling method to calculate electron paramagnetic resonance g-tensors from density matrix renormalization group wavefunctions. We apply the technique to compute g-tensors for the TiF3 and CuCl42- complexes, a [2Fe-2S] model of the active center of ferredoxins, and a Mn4CaO5 model of the S2 state of the oxygen evolving complex. These calculations raise the prospects of determining g-tensors in multireference calculations with a large number of open shells.

Automated Construction of Molecular Active Spaces from Atomic Valence Orbitals.

We introduce the atomic valence active space (AVAS), a simple and well-defined automated technique for constructing active orbital spaces for use in multiconfiguration and multireference (MR) electronic structure calculations. Concretely, the technique constructs active molecular orbitals capable of describing all relevant electronic configurations emerging from a targeted set of atomic valence orbitals (e.g., the metal d orbitals in a coordination complex). This is achieved via a linear transformation of the occupied and unoccupied orbital spaces from an easily obtainable single-reference wave function (such as from a Hartree-Fock or Kohn-Sham calculations) based on projectors to targeted atomic valence orbitals. We discuss the premises, theory, and implementation of the idea, and several of its variations are tested. To investigate the performance and accuracy, we calculate the excitation energies for various transition-metal complexes in typical application scenarios. Additionally, we follow the homolytic bond breaking process of a Fenton reaction along its reaction coordinate. While the described AVAS technique is not a universal solution to the active space problem, its premises are fulfilled in many application scenarios of transition-metal chemistry and bond dissociation processes. In these cases the technique makes MR calculations easier to execute, easier to reproduce by any user, and simplifies the determination of the appropriate size of the active space required for accurate results.

A state interaction spin-orbit coupling density matrix renormalization group method.

We describe a state interaction spin-orbit (SISO) coupling method using density matrix renormalization group (DMRG) wavefunctions and the spin-orbit mean-field (SOMF) operator. We implement our DMRG-SISO scheme using a spin-adapted algorithm that computes transition density matrices between arbitrary matrix product states. To demonstrate the potential of the DMRG-SISO scheme we present accurate benchmark calculations for the zero-field splitting of the copper and gold atoms, comparing to earlier complete active space self-consistent-field and second-order complete active space perturbation theory results in the same basis. We also compute the effects of spin-orbit coupling on the spin-ladder of the iron-sulfur dimer complex [Fe2S2(SCH3)4](3-), determining the splitting of the lowest quartet and sextet states. We find that the magnitude of the zero-field splitting for the higher quartet and sextet states approaches a significant fraction of the Heisenberg exchange parameter.