Subspace Methods for the Simulation of Molecular Response Properties on a Quantum Computer.

We explore Davidson methods for obtaining excitation energies and other linear response properties within the recently developed quantum self-consistent linear response (q-sc-LR) method. Davidson-type methods allow for obtaining only a few selected excitation energies without explicitly constructing the electronic Hessian since they only require the ability to perform Hessian-vector multiplications. We apply the Davidson method to calculate the excitation energies of hydrogen chains (up to H10) and analyze aspects of statistical noise for computing excitation energies on quantum simulators. Additionally, we apply Davidson methods for computing linear response properties such as static polarizabilities for H2, LiH, H2O, OH-, and NH3, and show that unitary coupled cluster outperforms classical projected coupled cluster for molecular systems with strong correlation. Finally, we formulate the Davidson method for damped (complex) linear response, with application to the nitrogen K-edge X-ray absorption of ammonia, and the C6 coefficients of H2, LiH, H2O, OH-, and NH3.

Quantum Equation of Motion with Orbital Optimization for Computing Molecular Properties in Near-Term Quantum Computing.

Determining the properties of molecules and materials is one of the premier applications of quantum computing. A major question in the field is how to use imperfect near-term quantum computers to solve problems of practical value. Inspired by the recently developed variants of the quantum counterpart of the equation-of-motion (qEOM) approach and the orbital-optimized variational quantum eigensolver (oo-VQE), we present a quantum algorithm (oo-VQE-qEOM) for the calculation of molecular properties by computing expectation values on a quantum computer. We perform noise-free quantum simulations of BeH2 in the series of STO-3G/6-31G/6-31G* basis sets and of H4 and H2O in 6-31G using an active space of four electrons and four spatial orbitals (8 qubits) to evaluate excitation energies, electronic absorption, and, for twisted H4, circular dichroism spectra. We demonstrate that the proposed algorithm can reproduce the results of conventional classical CASSCF calculations for these molecular systems.

Quantum Mechanical Versus Polarizable Embedding Schemes: A Study of the Xray Absorption Spectra of Aqueous Ammonia and Ammonium.

The X-ray absorption spectra of aqueous ammonia and ammonium are computed using a combination of coupled cluster singles and doubles (CCSD) with different quantum mechanical and molecular mechanical embedding schemes. Specifically, we compare frozen Hartree-Fock (HF) density embedding, polarizable embedding (PE), and polarizable density embedding (PDE). Integrating CCSD with frozen HF density embedding is possible within the CC-in-HF framework, which circumvents the conventional system-size limitations of standard coupled cluster methods. We reveal similarities between PDE and frozen HF density descriptions, while PE spectra differ significantly. By including approximate triple excitations, we also investigate the effect of improving the electronic structure theory. The spectra computed using this approach show an improved intensity ratio compared to CCSD-in-HF. Charge transfer analysis of the excitations shows the local character of the pre-edge and main-edge, while the post-edge is formed by excitations delocalized over the first solvation shell and beyond.

Which Options Exist for NISQ-Friendly Linear Response Formulations?

Linear response (LR) theory is a powerful tool in classic quantum chemistry crucial to understanding photoinduced processes in chemistry and biology. However, performing simulations for large systems and in the case of strong electron correlation remains challenging. Quantum computers are poised to facilitate the simulation of such systems, and recently, a quantum linear response formulation (qLR) was introduced [Kumar et al., J. Chem. Theory Comput. 2023, 19, 9136-9150]. To apply qLR to near-term quantum computers beyond a minimal basis set, we here introduce a resource-efficient qLR theory, using a truncated active-space version of the multiconfigurational self-consistent field LR ansatz. Therein, we investigate eight different near-term qLR formalisms that utilize novel operator transformations that allow the qLR equations to be performed on near-term hardware. Simulating excited state potential energy curves and absorption spectra for various test cases, we identify two promising candidates, dubbed "proj LRSD" and "all-proj LRSD".

Simulating X-ray Absorption Spectroscopy in Challenging Environments: Methodological Insights from Water-Solvated Ammonia and Ammonium Systems.

Core-electron excitations in solvated systems, influenced by solvent geometry and hydrogen bonding, make X-ray absorption spectroscopy (XAS) a valuable tool for assessing solvent-solute interactions. However, calculating XAS spectra with electronic-structure methods has proven challenging due to a delicate interplay between correlation and solvation effects. This study provides a computational procedure for XAS modeling in solvated systems, with water-solvated ammonia and ammonium systems serving as probes. Exploring methodological challenges, we investigate explicit embedding models, specifically the polarizable embedding family, including polarizable density embedding and extended polarizable density embedding. Our linear-response time-dependent density functional theory (LR-TDDFT) XAS calculations reveal the efficiency of this approach, with extended polarizable density embedding emerging as a robust improvement over polarizable density embedding. Contrary to some recent literature, our study challenges the belief that LR-TDDFT cannot accurately describe XAS spectra of ammonia and ammonium solvated in water.

The variational quantum eigensolver self-consistent field method within a polarizable embedded framework.

We formulate and implement the Variational Quantum Eigensolver Self Consistent Field (VQE-SCF) algorithm in combination with polarizable embedding (PE), thereby extending PE to the regime of quantum computing. We test the resulting algorithm, PE-VQE-SCF, on quantum simulators and demonstrate that the computational stress on the quantum device is only slightly increased in terms of gate counts compared to regular VQE-SCF. On the other hand, no increase in shot noise was observed. We illustrate how PE-VQE-SCF may lead to the modeling of real chemical systems using a simulation of the reaction barrier of the Diels-Alder reaction between furan and ethene as an example.

Color Tuning in Bovine Rhodopsin through Polarizable Embedding.

Bovine rhodopsin is among the most studied proteins in the rhodopsin family. Its primary activation mechanism is the photoisomerization of 11-cis retinal, triggered by the absorption of a UV-visible photon. Different mutants of the same rhodopsin show different absorption wavelengths due to the influence of the specific amino acid residues forming the cavity in which the retinal chromophore is embedded, and rhodopsins activated at different wavelengths are, for example, exploited in the field of optogenetics. In this letter, we present a procedure for systematically investigating color tuning in models of bovine rhodopsin and a set of its mutants embedded in a membrane bilayer. Vertical excitation energy calculations were carried out with the polarizable embedding potential for describing the environment surrounding the chromophore. We show that polarizable embedding outperformed regular electrostatic embedding in determining both the vertical excitation energies and associated oscillator strengths of the systems studied.

Accuracy of One- and Two-Photon Intensities with the Extended Polarizable Density Embedding Model.

The recently developed extended polarizable density embedding (PDE-X) model is evaluated for the spectroscopic properties of organic chromophores solvated in water, including both one- and two-photon absorption properties. The PDE-X embedding model systematically improves vertical excitation energies over the preceding polarizable density embedding model (PDE). PDE-X shows more modest improvements over existing embedding models for oscillator strengths and two-photon absorption cross-sections, which are more sensitive properties. We argue that the origin of these discrepancies is related to the description of polarization effects, suggesting directions for future development of the embedding model.

Natamycin interferes with ergosterol-dependent lipid phases in model membranes.

Natamycin is an antifungal polyene macrolide that is used as a food preservative but also to treat fungal keratitis and other yeast infections. In contrast to other polyene antimycotics, natamycin does not form ion pores in the plasma membrane, but its mode of action is poorly understood. Using nuclear magnetic resonance (NMR) spectroscopy of deuterated sterols, we find that natamycin slows the mobility of ergosterol and cholesterol in liquid-ordered (Lo) membranes to a similar extent. This is supported by molecular dynamics (MD) simulations, which additionally reveal a strong impact of natamycin dimers on sterol dynamics and water permeability. Interference with sterol-dependent lipid packing is also reflected in a natamycin-mediated increase in membrane accessibility for dithionite, particularly in bilayers containing ergosterol. NMR experiments with deuterated sphingomyelin (SM) in sterol-containing membranes reveal that natamycin reduces phase separation and increases lipid exchange in bilayers with ergosterol. In ternary lipid mixtures containing monounsaturated phosphatidylcholine, saturated SM, and either ergosterol or cholesterol, natamycin interferes with phase separation into Lo and liquid-disordered (Ld) domains, as shown by NMR spectroscopy. Employing the intrinsic fluorescence of natamycin in ultraviolet-sensitive microscopy, we can visualize the binding of natamycin to giant unilamellar vesicles (GUVs) and find that it has the highest affinity for the Lo phase in GUVs containing ergosterol. Our results suggest that natamycin specifically interacts with the sterol-induced ordered phase, in which it disrupts lipid packing and increases solvent accessibility. This property is particularly pronounced in ergosterol containing membranes, which could underlie the selective antifungal activity of natamycin.

Theoretical and Numerical Comparison of Quantum- and Classical Embedding Models for Optical Spectra.

Quantum-mechanical (QM) and classical embedding models approximate a supermolecular quantum-chemical calculation. This is particularly useful when the supermolecular calculation has a size that is out of reach for present QM models. Although QM and classical embedding methods share the same goal, they approach this goal from different starting points. In this study, we compare the polarizable embedding (PE) and frozen-density embedding (FDE) models. The former is a classical embedding model, whereas the latter is a density-based QM embedding model. Our comparison focuses on solvent effects on optical spectra of solutes. This is a typical scenario where super-system calculations including the solvent environment become prohibitively large. We formulate a common theoretical framework for PE and FDE models and systematically investigate how PE and FDE approximate solvent effects. Generally, differences are found to be small, except in cases where electron spill-out becomes problematic in the classical frameworks. In these cases, however, atomic pseudopotentials can reduce the electron-spill-out issue.

Embedding Beyond Electrostatics: The Extended Polarizable Density Embedding Model.

The polarizable density embedding (PDE) model is a focused QM/QM fragment-based embedding model designed to model solvation effects on molecular properties. We extend the PDE model to include exchange and nonadditive exchange-correlation (for DFT) in the embedding potential in addition to the existing electrostatic, polarization, and nonelectrostatic effects already present. The resulting model, termed PDE-X, yields localized electronic excitation energies that accurately capture the range dependence of the solvent interaction and gives close agreement with full quantum mechanical (QM) results, even when using minimal QM regions. We show that the PDE-X embedding description consistently improves the accuracy of excitation energies for a diverse set of organic chromophores. The improved embedding description leads to systematic solvent effects that do not average out when applying configurational sampling.

Nuclear Magnetic Shielding Constants with the Polarizable Density Embedding Model.

We extend the polarizable density embedding (PDE) model to support the calculation of nuclear magnetic resonance (NMR) shielding constants using gauge-including atomic orbitals (GIAOs) within a density functional theory (DFT) framework. The PDE model divides the total system into fragments, describing some by quantum mechanics (QM) and the others through an embedding model. The PDE model uses anisotropic polarizabilities, inter-fragment two-electron Coulomb integrals, and a non-local repulsion operator to emulate the QM effects. The terms involving Coulomb integrals are straightforwardly extended with GIAOs. In contrast, we consider two approaches to handle the gauge dependency of the non-local operator, employing either simple symmetrization or a gauge transformation. We find the latter approach to be most stable with respect to increasing the basis set size of the QM region. We examine the accuracy of the PDE model for calculating NMR shielding constants on several solutes in a water solution. The performance is compared with the classical polarizable embedding (PE) model in addition to supermolecular reference calculations. Based on these systems, we address the basis set convergence characteristics and the QM region size requirements. Furthermore, we investigate the performance of the PDE model for a system with significant electron spill-out. In many cases, we find that the PDE model outperforms the PE model, especially regarding the accuracy of nuclear shielding constants when using small QM region sizes and in systems with significant electron spill-out.

Multiconfigurational SCF and Short-Range DFT Combined with Polarizable Density Embedding: Comparison of Linear-Response and State-Specific Solvatochromic Shifts of Acrolein and Para-nitrophenolate in Water.

The polarizable density embedding model is combined with the multiconfigurational self-consistent field and MC-srDFT electronic structure methods to calculate solvatochromic shifts of the n-π* absorption of acrolein and the π-π* absorption of the para-nitrophenolate anion in aqueous solution. Differences between linear-response (LR) and state-specific (SS) solvent shifts are analyzed by assessing the contributions of different terms in the solvent potential. This comparison shows that the differences are not only due to the intrinsically different response of LR and SS excitation energies to the polarizability of the environment but also due to a different response to the static part of the environment potential. These observations show that even in nonpolarizable environments, LR and SS calculations based on SCF (orbital optimization) methods do not necessarily agree on the spectral shift. The difference can be as large as, or even dominate, the difference due to dynamical polarization.

Natamycin sequesters ergosterol and interferes with substrate transport by the lysine transporter Lyp1 from yeast.

Natamycin is a polyene macrolide, widely employed to treat fungal keratitis and other yeast infections as well as to protect food products against fungal molds. In contrast to other polyene macrolides, such as nystatin or amphotericin B, natamycin does not form pores in yeast membranes, and its mode of action is not well understood. Here, we have employed a variety of spectroscopic methods, computational modeling, and membrane reconstitution to study the molecular interactions of natamycin underlying its antifungal activity. We find that natamycin forms aggregates in an aqueous solution with strongly altered optical properties compared to monomeric natamycin. Interaction of natamycin with model membranes results in a concentration-dependent fluorescence increase which is more pronounced for ergosterol- compared to cholesterol-containing membranes up to 20 mol% sterol. Evidence for formation of specific ergosterol-natamycin complexes in the bilayer is provided. Using nuclear magnetic resonance (NMR) and electron spin resonance (ESR) spectroscopy, we find that natamycin sequesters sterols, thereby interfering with their well-known ability to order acyl chains in lipid bilayers. This effect is more pronounced for membranes containing the sterol of fungi, ergosterol, compared to those containing mammalian cholesterol. Natamycin interferes with ergosterol-dependent transport of lysine by the yeast transporter Lyp1, which we propose to be due to the sequestering of ergosterol, a mechanism that also affects other plasma membrane proteins. Our results provide a mechanistic explanation for the selective antifungal activity of natamycin, which can set the stage for rational design of novel polyenes in the future.

Mechanism behind Polysorbates' Inhibitory Effect on P-Glycoprotein.

Much effort has been invested in the search for modulators of membrane transport proteins such as P-glycoprotein (P-gp) to improve drug bioavailability and reverse multidrug resistance in cancer. Nonionic surfactants, a class of pharmaceutical excipients, are known to inhibit such proteins, but knowledge about the exact mechanism of this inhibition is scarce. Here, we perform multiscale molecular dynamics simulations of one of these surfactants, polysorbate 20 (PS20), to reveal the behavior of such compounds on the molecular level and thereby discover the molecular mechanism of the P-gp inhibition. We show that the amphiphilic headgroup of PS20 is too hydrophobic to partition in the water phase, which drives the binding of PS20 to the amphiphilic drug-binding domain of P-gp and thereby causes the inhibition of the protein. Based on our findings, we conclude that PS20 primarily inhibits P-gp through direct binding to the drug-binding domain (DBD) from the extracellular leaflet.

Fast Approximate but Accurate QM/MM Interactions for Polarizable Embedding.

The coupling between the quantum (QM) and classical (MM) regions is often one of the computational bottlenecks when applying polarizable QM/MM to computational spectroscopy. In this Article, we explore three strategies to approximate the QM/MM coupling based on multipole expansion techniques. The implementations of these approximations are benchmarked in terms of both accuracy and computational efficiency and are furthermore applied to the calculation of spectroscopic properties including both one- and two-photon absorption strengths. We show that the proposed strategies provide significant computational savings without compromising the accuracy of the calculated spectroscopic properties.

Nitrogen K-Edge X-ray Absorption Spectra of Ammonium and Ammonia in Water Solution: Assessing the Performance of Polarizable Embedding Coupled Cluster Methods.

The recent development of liquid jet and liquid leaf sample delivery systems allows for accurate measurements of soft X-ray absorption spectra in transmission mode of solutes in a liquid environment. As this type of measurement becomes increasingly accessible, there is a strong need for reliable theoretical methods for assisting in the interpretation of the experimental data. Coupled cluster methods have been extensively developed over the past decade to simulate X-ray absorption in the gas phase. Their performance for solvated species, on the contrary, remains largely unexplored. Here, we investigate the current state of the art of coupled cluster modeling of nitrogen K-edge X-ray absorption of aqueous ammonia and ammonium based on quantum mechanics/molecular mechanics, where both the level of coupled cluster calculations and polarizable embedding are scrutinized. The results are compared to existing experimental data as well as simulations based on transition potential density functional theory.

Photophysical and Structural Characterization of Intrinsically Fluorescent Sterol Aggregates.

Self-association of cholesterol into aggregates and crystals is a hallmark of developing atherosclerosis. Intrinsically fluorescent sterols, such as dehydroergosterol (DHE), can be used to study sterol aggregation by fluorescence spectroscopy and microscopy, but a thorough understanding of DHE's photophysical and structural properties in the aggregated state is missing. Here, we show that DHE forms submicron fluorescent aggregates when evaporated from an ethanol solution. Using atomic force microscopy, we find that DHE, like cholesterol, forms compact oblate-shape aggregates of <100 nm in diameter. DHE's fluorescence is lowered in the aggregate compared to the monomeric form, and characteristic spectral changes accompany the aggregation process. Electronic structure calculations of DHE dimers in water indicate that Frenkel-type exciton coupling contributes to the lowered DHE fluorescence in the aggregates. Using molecular dynamics (MD) simulations, we show that DHE forms compact aggregates on the nanosecond scale and with strong intermolecular attraction, in which a broad range of orientations, and therefore electronic couplings, will take place. Tight packing of DHE in aggregates also lowers the apparent absorption cross section, further reducing the molecular brightness of the aggregates. Our results pave the way for systematic solubility studies of intrinsically fluorescent analogues of biologically relevant sterols.

Efficient Open-Source Implementations of Linear-Scaling Polarizable Embedding: Use Octrees to Save the Trees.

We present open-source implementations of the linear-scaling fast multipole method (FMM) within the polarizable embedding (PE) model for efficient treatment of large polarizable environments in computational spectroscopy simulations. The implementations are tested for accuracy, efficiency, and usability on model systems as well as more realistic biomolecular systems. We explain how FMM parameters affect the calculation of molecular properties and show that PE calculations employing FMM can be carried out in a black-box manner. The efficiency of the linear-scaling approach is demonstrated by simulating the UV/vis spectrum of a chromophore in an environment of more than 1 million polarizable sites. Our implementations are interfaced to several open-source quantum chemistry programs, making computational spectroscopy simulations within the PE model and FMM available to a large variety of methods and a broad user base.

Computational and photophysical characterization of a Laurdan malononitrile derivative.

The malononitrile group is considered one of the strongest natural electron-withdrawing groups in a chemist's arsenal. However, surprisingly little is known about how this group functions in push-pull fluorophores. In a recent computational study, we reported that replacing the ketone group of the traditional push-pull dye Laurdan with a malononitrile group significantly improves the optical properties while retaining the membrane behavior of the parent molecule Laurdan. Motivated by these results, we report here the synthesis and photophysical characterization of the said compound, 6-(1-undecyl-2,2-dicyanovinyl)-N,N-dimethyl-2-naphthylamine (CN-Laurdan). To our surprise, this new CN-Laurdan probe is found to be much less bright than the parent Laurdan due to a large drop in the fluorescence quantum yield. Using computational methods, we determine that the origin of this low quantum yield is related to the existence of a non-radiative decay pathway related to a rotation of the malononitrile moiety, suggesting that the molecule could nonetheless function very well as a molecular rotor. We confirm experimentally that CN-Laurdan functions as a molecular rotor by measuring the quantum yield in methanol/glycerol mixtures of increasing viscosity. Specifically, we found a consistent increase in the quantum yield across the entire range of tested viscosities.