Water inside the Selectivity Filter of a K+ Ion Channel: Structural Heterogeneity, Picosecond Dynamics, and Hydrogen Bonding.

Water inside biological ion channels regulates the key properties of these proteins, such as selectivity, ion conductance, and gating. In this article, we measure the picosecond spectral diffusion of amide I vibrations of an isotope-labeled KcsA potassium channel using two-dimensional infrared (2D IR) spectroscopy. By combining waiting time (100-2000 fs) 2D IR measurements of the KcsA channel including 13C18O isotope-labeled Val76 and Gly77 residues with molecular dynamics simulations, we elucidated the site-specific dynamics of water and K+ ions inside the selectivity filter of KcsA. We observe inhomogeneous 2D line shapes with extremely slow spectral diffusion. Our simulations quantitatively reproduce the experiments and show that water is the only component with any appreciable dynamics, whereas K+ ions and the protein are essentially static on a picosecond timescale. By analyzing simulated and experimental vibrational frequencies, we find that water in the selectivity filter can be oriented to form hydrogen bonds with adjacent or nonadjacent carbonyl groups with the reorientation timescales being three times slower and comparable to that of water molecules in liquid, respectively. Water molecules can reside in the cavity sufficiently far from carbonyls and behave essentially like "free" gas-phase-like water with fast reorientation times. Remarkably, no interconversion between these configurations was observed on a picosecond timescale. These dynamics are in stark contrast with liquid water, which remains highly dynamic even in the presence of ions at high concentrations.

Water inside the selectivity filter of a K+ ion channel: structural heterogeneity, picosecond dynamics, and hydrogen-bonding.

Water inside biological ion channels regulates the key properties of these proteins such as selectivity, ion conductance, and gating. In this Article we measure the picosecond spectral diffusion of amide I vibrations of an isotope labeled KcsA potassium channel using two-dimensional infrared (2D IR) spectroscopy. By combining waiting time (100 - 2000 fs) 2D IR measurements of the KcsA channel including 13C18O isotope labeled Val76 and Gly77 residues with molecular dynamics simulations, we elucidated the site-specific dynamics of water and K+ ions inside the selectivity filter of KcsA. We observe inhomogeneous 2D lineshapes with extremely slow spectral diffusion. Our simulations quantitatively reproduce the experiments and show that water is the only component with any appreciable dynamics, whereas K+ ions and the protein are essentially static on a picosecond timescale. By analyzing simulated and experimental vibrational frequencies, we find that water in the selectivity filter can be oriented to form hydrogen bonds with adjacent, or non-adjacent carbonyl groups with the reorientation timescales being three times slower and comparable to that of water molecules in liquid, respectively. Water molecules can reside in the cavity sufficiently far from carbonyls and behave essentially like "free" gas-phase-like water with fast reorientation times. Remarkably, no interconversion between these configurations were observed on a picosecond timescale. These dynamics are in stark contrast with liquid water that remains highly dynamic even in the presence of ions at high concentrations.

Novel Computational Chemistry Infrastructure for Simulating Astatide in Water: From Basis Sets to Force Fields Using Particle Swarm Optimization.

Using the example of astatine, the heaviest naturally occurring halogen whose isotope At-211 has promising medical applications, we propose a new infrastructure for large-scale computational models of heavy elements with strong relativistic effects. In particular, we focus on developing an accurate force field for At- in water based on reliable relativistic density functional theory (DFT) calculations. To ensure the reliability of such calculations, we design novel basis sets for relativistic DFT, via the particle swarm optimization algorithm to optimize the coefficients of the new basis sets and the polarization-consistent basis set idea's extension to heavy elements to eliminate the basis set error from DFT calculations. The resulting basis sets enable the well-grounded evaluation of relativistic DFT against "gold-standard" CCSD(T) results. Accounting for strong relativistic effects, including spin-orbit interaction, via our redesigned infrastructure, we elucidate a noticeable dissimilarity between At- and I- in halide-water force field parameters, radial distribution functions, diffusion coefficients, and hydration energies. This work establishes the framework for the systematic development of polarization-consistent basis sets for relativistic DFT and accurate force fields for molecular dynamics simulations to be used in large-scale models of complex molecular systems with elements from the bottom of the periodic table, including actinides and even superheavy elements.

Probing Ion Configurations in the KcsA Selectivity Filter with Single-Isotope Labels and 2D IR Spectroscopy.

The potassium ion (K+) configurations of the selectivity filter of the KcsA ion channel protein are investigated with two-dimensional infrared (2D IR) spectroscopy of amide I vibrations. Single 13C-18O isotope labels are used, for the first time, to selectively probe the S1/S2 or S2/S3 binding sites in the selectivity filter. These binding sites have the largest differences in ion occupancy in two competing K+ transport mechanisms: soft-knock and hard-knock. According to the former, water molecules alternate between K+ ions in the selectivity filter while the latter assumes that K+ ions occupy the adjacent sites. Molecular dynamics simulations and computational spectroscopy are employed to interpret experimental 2D IR spectra. We find that in the closed conductive state of the KcsA channel, K+ ions do not occupy adjacent binding sites. The experimental data is consistent with simulated 2D IR spectra of soft-knock ion configurations. In contrast, the simulated spectra for the hard-knock ion configurations do not reproduce the experimental results. 2D IR spectra of the hard-knock mechanism have lower frequencies, homogeneous 2D lineshapes, and multiple peaks. In contrast, ion configurations of the soft-knock model produce 2D IR spectra with a single peak at a higher frequency and inhomogeneous lineshape. We conclude that under equilibrium conditions, in the absence of transmembrane voltage, both water and K+ ions occupy the selectivity filter of the KcsA channel in the closed conductive state. The ion configuration is central to the mechanism of ion transport through potassium channels.

Combinational Vibration Modes in H2O/HDO/D2O Mixtures Detected Thanks to the Superior Sensitivity of Femtosecond Stimulated Raman Scattering.

Overtones and combinational modes frequently play essential roles in ultrafast vibrational energy relaxation in liquid water. However, these modes are very weak and often overlap with fundamental modes, particularly in isotopologues mixtures. We measured VV and HV Raman spectra of H2O and D2O mixtures with femtosecond stimulated Raman scattering (FSRS) and compared the results with calculated spectra. Specifically, we observed the mode at around 1850 cm-1 and assigned it to H-O-D bend + rocking libration. Second, we found that the H-O-D bend overtone band and the OD stretch + rocking libration combination band contribute to the band located between 2850 and 3050 cm-1. Furthermore, we assigned the broad band located between 4000 and 4200 cm-1 to be composed of combinational modes of high-frequency OH stretching modes with predominantly twisting and rocking librations. These results should help in a proper interpretation of Raman spectra of aqueous systems as well as in the identification of vibrational relaxation pathways in isotopically diluted water.

Convolutional Neural Networks for Long Time Dissipative Quantum Dynamics.

Exact numerical simulations of dynamics of open quantum systems often require immense computational resources. We demonstrate that a deep artificial neural network composed of convolutional layers is a powerful tool for predicting long-time dynamics of open quantum systems provided the preceding short-time evolution of a system is known. The neural network model developed in this work simulates long-time dynamics efficiently and accurately across different dynamical regimes from weakly damped coherent motion to incoherent relaxation. The model was trained on a data set relevant to photosynthetic excitation energy transfer and can be deployed to study long-lasting quantum coherence phenomena observed in light-harvesting complexes. Furthermore, our model performs well for the initial conditions different than those used in the training. Our approach reduces the required computational resources for long-time simulations and holds the promise for becoming a valuable tool in the study of open quantum systems.

Unusually strong hydrogen bond cooperativity in particular (H2O)20 clusters.

Drawing upon an intuitive charge-transfer-based picture of hydrogen bonding, we demonstrate that cooperativity effects acting in concert can lead to unusually strong hydrogen bonds in neutral water clusters. The structure, vibrational, and NMR properties of a (H2O)20 pentagonal dodecahedron cluster containing such a strong hydrogen bond were studied using second-order perturbation theory and density functional theory. The hydrogen bond length was found to be shorter than 2.50 Å. A large redshift of over 2000 cm-1 with respect to the isolated water molecule was predicted for the OH stretching frequency of the donor water molecule. A large downfield shift to 13.5 ppm of the isotropic part of the 1H magnetic shielding tensor together with an unusually large shielding anisotropy of 49.9 ppm was obtained. The hydrogen bond energy was calculated using symmetry-adapted perturbation theory and was found to be more than three times stronger than a typical hydrogen bond in liquid water.

Dephasing and Decoherence in Vibrational and Electronic Line Shapes.

Absorption and emission line shapes of vibrational and electronic transitions in liquids are broadened by interactions with the "bath" (in this case, the rotational and translational degrees of freedom of all the molecules in the liquid). If these degrees of freedom are treated classically, the broadening process is often known as dephasing. If, on the other hand, the bath degrees of freedom are instead treated quantum mechanically, there is additional broadening due to what is known in the chemical-physics literature as decoherence. The question addressed in this paper is the relative importance of decoherence (bath quantum effects) and dephasing. We present general developments of this subject for absorption and emission line shapes, discover several new relationships connecting classical and quantum treatments of the bath, and also consider the Stokes shift (difference in peak frequencies in absorption and emission). We next draw some general conclusions by considering a model system whose transition-frequency time-correlation function has only one bath time scale. We then consider a realistic system of the vibrational OH stretch transition of dilute HOD in liquid D2O at room temperature. For this system, we conclude that bath quantum effects are not very important, except for the Stokes shift. More generally, we argue that this is the case for many vibrational and most electronic transitions in room-temperature liquids.

IR Spectroscopy Can Reveal the Mechanism of K+ Transport in Ion Channels.

Ion channels like KcsA enable ions to move across cell membranes at near diffusion-limited rates and with very high selectivity. Various mechanisms have been proposed to explain this phenomenon. Broadly, there is disagreement among the proposed mechanisms about whether ions occupy adjacent sites in the channel during the transport process. Here, using a mixed quantum-classical approach to calculate theoretical infrared spectra, we propose a set of infrared spectroscopy experiments that can discriminate between mechanisms with and without adjacent ions. These experiments differ from previous ones in that they independently probe specific ion binding sites within the selectivity filter. When ions occupy adjacent sites in the selectivity filter, the predicted spectra are significantly redshifted relative to when ions do not occupy adjacent sites. Comparisons between theoretical and experimental peak frequencies will therefore discriminate the mechanisms.

Machine Learning for Vibrational Spectroscopic Maps.

Maps that relate spectroscopic properties of a vibrational mode and collective solvent coordinates have proven useful in theoretical vibrational spectroscopy of condensed-phase systems. It has been realized that the predictive power of such an approach is limited and there is no clear systematic way to improve its accuracy. Here, we propose an adaptation of Δ-machine-learning methodology that goes beyond the spectroscopic maps. The machine-learning part of our approach combines Gaussian process regression used to generate the data set with an artificial neural network used to predict spectroscopic properties of interest. A specific application to the OH-stretch frequencies and transition dipoles of water is presented. Our method approximates these properties about two times more accurately than the spectroscopic-maps-only-based approach. Our results suggest that the new approach may become useful in the study of vibrational spectroscopy of condensed-phase systems.

OH-Stretch Raman Multivariate Curve Resolution Spectroscopy of HOD/H2O Mixtures.

Recently, in an attempt to quantify the role of intermolecular OH stretching vibrational couplings in liquid water, experimental Raman spectra of HOD/H2O mixtures were analyzed using the multivariate curve resolution (Raman-MCR) algorithm. This algorithm allowed for the separation of the HOD solute-correlated spectrum from the spectrum of bulk water. The former spectrum highlights features arising from HOD itself as well as from perturbations it induces on the surrounding H2O molecules. In this work, we apply a mixed quantum-classical methodology developed in our group to simulate the isotropic Raman-MCR spectra of HOD/H2O mixtures. Our results illustrate that intermolecular coupling leads to broadening and a red shift of the OH stretching band, in good agreement with the experiment. Our theoretical analysis provides a molecular-level interpretation of Raman-MCR experiments on HOD/H2O mixtures, suggesting that perturbations affecting the OH stretching vibrational mode of HOD result from intermolecular vibrational coupling to surrounding H2O molecules extending well beyond the first solvation shell.

Fermi resonance in OH-stretch vibrational spectroscopy of liquid water and the water hexamer.

Vibrational spectroscopy of water contains a wealth of information about the structure and dynamics of this fascinating substance. Theoretical modeling of fundamental vibrational transitions in condensed water has proven difficult, and in many circumstances, one cannot reach even qualitative agreement with experiment. Due to the ability of water to form hydrogen bonds of various strengths, the OH stretching band spans several hundreds of wave numbers in the spectra, overlapping with the first overtone of the HOH bending band and triggering a resonance between these two vibrations. This effect, known as Fermi resonance, has been traditionally ignored in theoretical condensed-phase simulations due to the additional computational burden and its deemed low importance. Depending on a particular molecular environment, the Fermi resonance manifests itself from small spectral features in the spectra of liquid water to pronounced distinct peaks in the spectra of ice and water clusters. The goal of this work is to illustrate the effects of including the Fermi resonance coupling between the bending overtone and stretching fundamental vibrations in the mixed quantum-classical formalism developed by Skinner and co-workers on the IR and Raman spectra of liquid water and the water hexamer. We show that by adding the Fermi resonance coupling, we are able to reproduce the location of the peak and a shoulder on the red side of the IR spectrum as well as the bimodal structure of the polarized Raman spectrum of liquid water at 300 K. Very good agreement between theory and experiment is achieved for the IR spectra of the water hexamer as well. We suggest that the Fermi resonance should not be ignored if intricate features of spectra are of interest. In spite of these promising results obtained in the region of a spectrum where Fermi resonance is important, further development of spectroscopic maps is needed to improve agreement with the experiment outside of the frequency range affected by the Fermi resonance.

A comparative study of different methods for calculating electronic transition rates.

We present a comprehensive comparison of the following mixed quantum-classical methods for calculating electronic transition rates: (1) nonequilibrium Fermi's golden rule, (2) mixed quantum-classical Liouville method, (3) mean-field (Ehrenfest) mixed quantum-classical method, and (4) fewest switches surface-hopping method (in diabatic and adiabatic representations). The comparison is performed on the Garg-Onuchic-Ambegaokar benchmark charge-transfer model, over a broad range of temperatures and electronic coupling strengths, with different nonequilibrium initial states, in the normal and inverted regimes. Under weak to moderate electronic coupling, the nonequilibrium Fermi's golden rule rates are found to be in good agreement with the rates obtained via the mixed quantum-classical Liouville method that coincides with the fully quantum-mechanically exact results for the model system under study. Our results suggest that the nonequilibrium Fermi's golden rule can serve as an inexpensive yet accurate alternative to Ehrenfest and the fewest switches surface-hopping methods.

Nonadiabatic Dynamics via the Symmetrical Quasi-Classical Method in the Presence of Anharmonicity.

The symmetrical quasi-classical (SQC) method recently proposed by Miller and Cotton allows one to simulate nonadiabatic dynamics based on an algorithm with classical-like scaling with respect to system size. This is made possible by casting the electronic degrees of freedom in terms of mapping variables that can be propagated in a classical-like manner. While SQC was shown to be rather accurate when applied to benchmark models with harmonic electronic potential energy surfaces, it was also found to become inaccurate and to suffer numerical instabilities when applied to anharmonic systems. In this paper, we propose an extended SQC (E-SQC) methodology for overcoming those discrepancies by describing the anharmonic nuclear modes, which are coupled to the electronic degrees of freedom, in terms of classical-like mapping variables. The accuracy of E-SQC relative to standard SQC is demonstrated on benchmark models with quartic and Morse potential energy surfaces.

Combining Density Functional Theory and Green's Function Theory: Range-Separated, Nonlocal, Dynamic, and Orbital-Dependent Hybrid Functional.

We present a rigorous framework which combines single-particle Green's function theory with density functional theory based on a separation of electron-electron interactions into short- and long-range components. Short-range contribution to the total energy and exchange-correlation potential is provided by a density functional approximation, while the long-range contribution is calculated using an explicit many-body Green's function method. Such a hybrid results in a nonlocal, dynamic, and orbital-dependent exchange-correlation functional of a single-particle Green's function. In particular, we present a range-separated hybrid functional called srSVWN5-lrGF2 which combines the local-density approximation and the second-order Green's function theory. We illustrate that similarly to density functional approximations, the new functional is weakly basis-set dependent. Furthermore, it offers an improved description of the short-range dynamic correlation. The many-body contribution to the functional mitigates the many-electron self-interaction error present in many density functional approximations and provides a better description of molecular properties. Additionally, we illustrate that the new functional can be used to scale down the self-energy and, therefore, introduce an additional sparsity to the self-energy matrix that in the future can be exploited in calculations for large molecules or periodic systems.

Accurate Long-Time Mixed Quantum-Classical Liouville Dynamics via the Transfer Tensor Method.

In this Letter, we combine the recently introduced transfer tensor method with the mixed quantum-classical Liouville method. The resulting protocol provides an accurate, general, flexible and robust new route for simulating the reduced dynamics of the quantum subsystem for arbitrarily long times, starting with computationally feasible short-time mixed quantum-classical Liouville dynamical maps. The accuracy and feasibility of the methodology are demonstrated on a spin-boson benchmark model.

Rigorous Ab Initio Quantum Embedding for Quantum Chemistry Using Green's Function Theory: Screened Interaction, Nonlocal Self-Energy Relaxation, Orbital Basis, and Chemical Accuracy.

We present a detailed discussion of the self-energy embedding theory (SEET), which is a quantum embedding scheme allowing us to describe a chosen subsystem very accurately while keeping the description of the environment at a lower level. We apply SEET to molecular examples where our chosen subsystem is made out of a set of strongly correlated orbitals while the weakly correlated orbitals constitute an environment. Consequently, a highly accurate method is used to calculate the self-energy for the system, while a lower-level method is employed to find the self-energy for the environment. Such a self-energy separation is very general, and to make the SEET procedure applicable to multiple systems, a detailed and practical procedure for the evaluation of the system and environment self-energy is necessary. We list all of the intricacies for one of the possible procedures while focusing our discussion on many practical implementation aspects such as the choice of best orbital basis, impurity solver, and many steps necessary to reach chemical accuracy. Finally, on a set of carefully chosen molecular examples, we demonstrate that SEET, which is a controlled, systematically improvable Green's function method, can be as accurate as established wave function quantum chemistry methods.

Efficient Temperature-Dependent Green's Function Methods for Realistic Systems: Using Cubic Spline Interpolation to Approximate Matsubara Green's Functions.

The popular, stable, robust, and computationally inexpensive cubic spline interpolation algorithm is adopted and used for finite temperature Green's function calculations of realistic systems. We demonstrate that with appropriate modifications the temperature dependence can be preserved while the Green's function grid size can be reduced by about 2 orders of magnitude by replacing the standard Matsubara frequency grid with a sparser grid and a set of interpolation coefficients. We benchmarked the accuracy of our algorithm as a function of a single parameter sensitive to the shape of the Green's function. Through numerous examples, we confirmed that our algorithm can be utilized in a systematically improvable, controlled, and black-box manner and highly accurate one- and two-body energies and one-particle density matrices can be obtained using only around 5% of the original grid points. Additionally, we established that to improve accuracy by an order of magnitude, the number of grid points needs to be doubled, whereas for the Matsubara frequency grid, an order of magnitude more grid points must be used. This suggests that realistic calculations with large basis sets that were previously out of reach because they required enormous grid sizes may now become feasible.

Efficient Temperature-Dependent Green's Functions Methods for Realistic Systems: Compact Grids for Orthogonal Polynomial Transforms.

The Matsubara Green's function that is used to describe temperature-dependent behavior is expressed on a numerical grid. While such a grid usually has a couple of hundred points for low-energy model systems, for realistic systems with large basis sets the size of an accurate grid can be tens of thousands of points, constituting a severe computational and memory bottleneck. In this paper, we determine efficient imaginary time grids for the temperature-dependent Matsubara Green's function formalism that can be used for calculations on realistic systems. We show that, because of the use of an orthogonal polynomial transform, we can restrict the imaginary time grid to a few hundred points and reach micro-Hartree accuracy in the electronic energy evaluation. Moreover, we show that only a limited number of orthogonal polynomial expansion coefficients are necessary to preserve accuracy when working with a dual representation of the Green's function or self-energy and transforming between the imaginary time and frequency domain.

Fractional charge and spin errors in self-consistent Green's function theory.

We examine fractional charge and spin errors in self-consistent Green's function theory within a second-order approximation (GF2). For GF2, it is known that the summation of diagrams resulting from the self-consistent solution of the Dyson equation removes the divergences pathological to second-order Møller-Plesset (MP2) theory for strong correlations. In the language often used in density functional theory contexts, this means GF2 has a greatly reduced fractional spin error relative to MP2. The natural question then is what effect, if any, does the Dyson summation have on the fractional charge error in GF2? To this end, we generalize our previous implementation of GF2 to open-shell systems and analyze its fractional spin and charge errors. We find that like MP2, GF2 possesses only a very small fractional charge error, and consequently minimal many electron self-interaction error. This shows that GF2 improves on the critical failings of MP2, but without altering the positive features that make it desirable. Furthermore, we find that GF2 has both less fractional charge and fractional spin errors than typical hybrid density functionals as well as random phase approximation with exchange.