Assessment of MC-PDFT Excitation Energies for a Set of QM/MM Models of Rhodopsins

Molecules in Environments: Toward Systematic Quantum Embedding of Electrons and Drude Oscillators

We develop a quantum embedding method that enables accurate and efficient treatment of interactions between molecules and an environment, while explicitly including many-body correlations. The molecule is composed of classical nuclei and quantum electrons, whereas the environment is modeled via charged quantum harmonic oscillators. We construct a general Hamiltonian and introduce a variational Ansatz for the correlated ground state of the fully interacting molecule-environment system. This wave function is optimized via the variational Monte Carlo method and the ground state energy is subsequently estimated through the diffusion Monte Carlo method. The proposed scheme allows an explicit many-body treatment of electrostatic, polarization, and dispersion interactions between the molecule and the environment. We study solvation energies and excitation energies of benzene derivatives, obtaining excellent agreement with explicit ab initio calculations and experiments.

Assessment of the Electron Correlation Treatment on the Quantum-Classical Dynamics of Retinal Protonated Schiff Base Models: XMS-CASPT2, RMS-CASPT2, and REKS Methods

We compare the performance of three different multiconfigurational wave function-based electronic structure methods and two implementations of the spin-restricted ensemble-referenced Kohn-Sham (REKS) method. The study is characterized by three features: (i) it uses a small set of quantum-classical trajectories rather than potential energy surface mapping, (ii) it focuses, exclusively, on the photoisomerization of retinal protonated Schiff base models, and (iii) it probes the effect of both methyl substitution and the increase in length of the conjugate π-system. For each tested method, the corresponding analytical gradients are used to drive the quantum-classical (Tully's FSSH method) trajectory propagation, including the recent multistate XMS-CASPT2 and RMS-CASPT2 gradients. It is shown that while CASSCF, XMS-CASPT2, and RMS-CASPT2 yield consistent photoisomerization dynamics descriptions, REKS produces, in some of these systems, qualitatively different behavior that is attributed to a flatter and topographically different excited state potential energy surface. The origin of this behavior can be traced back to the effect of the employed density functional approximation. The above studies are further expanded by benchmarking, at the CASSCF and REKS levels, the electronic structure methods using a QM/MM model of the visual pigment rhodopsin.

Quantum Mechanics/Molecular mechanics calculations predict A1, not A2, is present in melanopsin (Opn4m) of red-eared slider turtles (Trachemys scripta elegans)

Melanopsin is a photopigment that plays a role in non-visual, light-driven, cellular processes such as modulation of circadian rhythms, retinal vascular development, and the pupillary light reflex (PLR). In this study, computational methods were used to understand which chromophore is harbored by melanopsin in red-eared slider turtles (Trachemys scripta elegans). In mammals, the vitamin A derivative 11-cis-retinal (A1) is the chromophore, which provides functionality for melanopsin. However, in red-eared slider turtles, a member of the reptilian class, the identity of the chromophore remains unclear. Red-eared slider turtles, similar to other freshwater vertebrates, possess visual pigments that harbor a different vitamin A derivative, 11-cis-3,4-didehydroretinal (A2), making their pigments more sensitive to red-light than blue-light, therefore, suggesting the chromophore to be the A2 derivative instead of the A1. To help resolve the chromophore identity, in this work, computational homology models of melanopsin in red-eared slider turtles were first constructed. Next, quantum mechanics/molecular mechanics (QM/MM) calculations were carried out to compare how A1 and A2 derivatives bind to melanopsin. Time dependent density functional theory (TDDFT) calculations were then used to determine the excitation energy of the pigments. Lastly, calculated excitation energies were compared to experimental spectral sensitivity data from responses by the irises of red-eared sliders. Contrary to what was expected, our results suggest that melanopsin in red-eared slider turtles is more likely to harbor the A1 chromophore than the A2. Furthermore, a glutamine (Q622.56) and tyrosine (Y853.28) residue in the chromophore binding pocket are shown to play a role in the spectral tuning of the chromophore.

Detailed analysis of distorted retinal and its interaction with surrounding residues in the K intermediate of bacteriorhodopsin

The K intermediate of proton pumping bacteriorhodopsin is the first intermediate generated after isomerization of retinal to the 13-cis form. Although various structures have been reported for the K intermediate until now, these differ from each other, especially in terms of the conformation of the retinal chromophore and its interaction with surrounding residues. We report here an accurate X-ray crystallographic analysis of the K structure. The polyene chain of 13-cis retinal is observed to be S-shaped. The side chain of Lys216, which is covalently bound to retinal via the Schiff-base linkage, interacts with residues, Asp85 and Thr89. In addition, the Nζ-H of the protonated Schiff-base linkage interacts with a residue, Asp212 and a water molecule, W402. Based on quantum chemical calculations for this K structure, we examine the stabilizing factors of distorted conformation of retinal and propose a relaxation manner to the next L intermediate.

Rhodopsins: An Excitingly Versatile Protein Species for Research, Development and Creative Engineering

The first member and eponym of the rhodopsin family was identified in the 1930s as the visual pigment of the rod photoreceptor cell in the animal retina. It was found to be a membrane protein, owing its photosensitivity to the presence of a covalently bound chromophoric group. This group, derived from vitamin A, was appropriately dubbed retinal. In the 1970s a microbial counterpart of this species was discovered in an archaeon, being a membrane protein also harbouring retinal as a chromophore, and named bacteriorhodopsin. Since their discovery a photogenic panorama unfolded, where up to date new members and subspecies with a variety of light-driven functionality have been added to this family. The animal branch, meanwhile categorized as type-2 rhodopsins, turned out to form a large subclass in the superfamily of G protein-coupled receptors and are essential to multiple elements of light-dependent animal sensory physiology. The microbial branch, the type-1 rhodopsins, largely function as light-driven ion pumps or channels, but also contain sensory-active and enzyme-sustaining subspecies. In this review we will follow the development of this exciting membrane protein panorama in a representative number of highlights and will present a prospect of their extraordinary future potential.

Evolution of the Automatic Rhodopsin Modeling (ARM) Protocol

In recent years, photoactive proteins such as rhodopsins have become a common target for cutting-edge research in the field of optogenetics. Alongside wet-lab research, computational methods are also developing rapidly to provide the necessary tools to analyze and rationalize experimental results and, most of all, drive the design of novel systems. The Automatic Rhodopsin Modeling (ARM) protocol is focused on providing exactly the necessary computational tools to study rhodopsins, those being either natural or resulting from mutations. The code has evolved along the years to finally provide results that are reproducible by any user, accurate and reliable so as to replicate experimental trends. Furthermore, the code is efficient in terms of necessary computing resources and time, and scalable in terms of both number of concurrent calculations as well as features. In this review, we will show how the code underlying ARM achieved each of these properties.

Nonadiabatic Molecular Dynamics by Multiconfiguration Pair-Density Functional Theory

We present the first implementation of multiconfiguration pair-density functional theory (MC-PDFT) ab initio molecular dynamics. MC-PDFT is a multireference electronic structure method that in many cases has a similar accuracy (or even better accuracy) the complete active space second-order perturbation theory (CASPT2) at a significantly lower computational cost. In this study, we introduced MC-PDFT analytical gradients into the SHARC molecular dynamics program for ab initio, nonadiabatic molecular dynamics simulations. We verify our implementation by examining the intersystem crossing dynamics of thioformaldehyde, and we observe excellent agreement with recent CASPT2 and experimental findings. Moreover, with MC-PDFT, we could perform dynamics simulations with the 12 electron in 10 orbitals active space that was computationally too expensive for direct dynamics with CASPT2.

Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory

Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn–Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin–orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in the nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals.

This feature article overviews recent work on active spaces, matrix product reference states, treatment of quasidegeneracy, hybrid theory, density-coherence functionals, machine-learned functionals, spin–orbit coupling, gradients, and dipole moments.

A multiconfiguration pair-density functional theory-based approach to molecular junctions

Due to their small size and unique properties, single-molecule electronics have long seen research interest from experimentalists and theoreticians alike. From a theoretical standpoint, modeling these systems using electronic structure theory can be difficult due to the importance of electron correlation in the determination of molecular properties, and this electron correlation can be computationally expensive to consider, particularly multiconfigurational correlation energy. In this work, we develop a new approach for the study of single-molecule electronic systems, denoted NEGF-MCPDFT, which combines multiconfiguration pair-density functional theory (MCPDFT) with the non-equilibrium Green's function formalism (NEGF). The use of MCPDFT with NEGF allows for the efficient inclusion of both static and dynamic electron correlations in the description of the junction's electronic structure. Complete active space self-consistent field wave functions are used as references in the MCPDFT calculation, and as with any active space method, effort must be made to determine the proper orbital character to include in the active space. We perform conductance and transmission calculations on a series of alkanes (predominantly single-configurational character) and benzyne (multiconfigurational character), exploring the role that active space selection has on the computed results. For the alkane junctions explored (where dynamic electron correlation dominates), the MCPDFT-NEGF results agree well with the DFT-NEGF results. For the benzyne junction (which has a significant static correlation), we see clear differences in the MCPDFT-NEGF and DFT-NEGF results and evidence that NEGF-MCPDFT is capturing additional electron correlation effects beyond those provided by the Perdew-Burke-Ernzerhof functional.

Analytic gradients for multiconfiguration pair-density functional theory with density fitting: Development and application to geometry optimization in the ground and excited states

Density fitting reduces the computational cost of both energy and gradient calculations by avoiding the computation and manipulation of four-index electron repulsion integrals. With this algorithm, one can efficiently optimize the geometries of large systems with an accurate multireference treatment. Here, we present the derivation of multiconfiguration pair-density functional theory for energies and analytic gradients with density fitting. Six systems are studied, and the results are compared to those obtained with no approximation to the electron repulsion integrals and to the results obtained by complete active space second-order perturbation theory. With the new approach, there is an increase in the speed of computation with a negligible loss in accuracy. Smaller grid sizes have also been used to reduce the computational cost of multiconfiguration pair-density functional theory with little effect on the optimized geometries and gradient values.

Mechanism of absorption wavelength shifts in anion channelrhodopsin-1 mutants

Using a quantum mechanical/molecular mechanical approach, we show the mechanisms of how the protein environment of Guillardia theta anion channelrhodopsin-1 (GtACR1) can shift the absorption wavelength. The calculated absorption wavelengths for GtACR1 mutants, M105A, C133A, and C237A are in agreement with experimentally measured wavelengths. Among 192 mutant structures investigated, mutations at Thr101, Cys133, Pro208, and Cys237 are likely to increase the absorption wavelength. In particular, T101A GtACR1 was expressed in HEK293T cells. The measured absorption wavelength is 10 nm higher than that of wild type, consistent with the calculated wavelength. (i) Removal of a polar residue from the Schiff base moiety, (ii) addition of a polar or acidic residue to the β-ionone ring moiety, and (iii) addition of a bulky residue to increase the planarity of the β-ionone and Schiff base moieties are the basis of increasing the absorption wavelength.

Insights into the Protein Functions and Absorption Wavelengths of Microbial Rhodopsins

Using a quantum mechanical/molecular mechanical approach, the absorption wavelength of the retinal Schiff base was calculated based on 13 microbial rhodopsin crystal structures. The results showed that the protein electrostatic environment decreases the absorption wavelength significantly in the cation-conducting rhodopsin but only slightly in the sensory rhodopsin. Among the microbial rhodopsins with different functions, the differences in the absorption wavelengths are caused by differences in the arrangement of the charged residues at the retinal Schiff base binding moiety, namely, one or two counterions at the three common positions. Among the microbial rhodopsins with similar functions, the differences in the polar residues at the retinal Schiff base binding site are responsible for the differences in the absorption wavelengths. Counterions contribute to an absorption wavelength shift of 50-120 nm, whereas polar groups contribute to a shift of up to ∼10 nm. It seems likely that protein function is directly associated with the absorption wavelength in microbial rhodopsins.

Embedding Methods for Quantum Chemistry: Applications from Materials to Life Sciences

Quantum mechanical embedding methods hold the promise to transform not just the way calculations are performed, but to significantly reduce computational costs and improve scaling for macro-molecular systems containing hundreds if not thousands of atoms. The field of embedding has grown increasingly broad with many approaches of different intersecting flavors. In this perspective, we lay out the methods into two streams: QM:MM and QM:QM, showcasing the advantages and disadvantages of both. We provide a review of the literature, the underpinning theories including our contributions, and we highlight current applications with select examples spanning both materials and life sciences. We conclude with prospects and future outlook on embedding, and our view on the use of universal test case scenarios for cross-comparisons of the many available (and future) embedding theories.

Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials

Optically active molecular materials, such as organic conjugated polymers and biological systems, are characterized by strong coupling between electronic and vibrational degrees of freedom. Typically, simulations must go beyond the Born-Oppenheimer approximation to account for non-adiabatic coupling between excited states. Indeed, non-adiabatic dynamics is commonly associated with exciton dynamics and photophysics involving charge and energy transfer, as well as exciton dissociation and charge recombination. Understanding the photoinduced dynamics in such materials is vital to providing an accurate description of exciton formation, evolution, and decay. This interdisciplinary field has matured significantly over the past decades. Formulation of new theoretical frameworks, development of more efficient and accurate computational algorithms, and evolution of high-performance computer hardware has extended these simulations to very large molecular systems with hundreds of atoms, including numerous studies of organic semiconductors and biomolecules. In this Review, we will describe recent theoretical advances including treatment of electronic decoherence in surface-hopping methods, the role of solvent effects, trivial unavoided crossings, analysis of data based on transition densities, and efficient computational implementations of these numerical methods. We also emphasize newly developed semiclassical approaches, based on the Gaussian approximation, which retain phase and width information to account for significant decoherence and interference effects while maintaining the high efficiency of surface-hopping approaches. The above developments have been employed to successfully describe photophysics in a variety of molecular materials.