Isoelectronic Theory for Cationic Radii

Ionic radii play a central role in all branches of chemistry, in geochemistry, solid-state physics, and biophysics. While authoritative compilations of experimental radii are available, their theoretical basis is unclear, and no quantitative derivation exists. Here we show how a quantitative calculation of ionic radii for cations with spherically symmetric charge distribution is obtained by charge-weighted averaging of outer and inner radii. The outer radius is the atomic (covalent) radius, and the inner is that of the underlying closed-shell orbital. The first is available from recent experimental compilations, whereas the second is calculated from a “modified Slater theory”, in which the screening (<i>S</i>) and effective principal quantum number (<i>n</i>*) were previously obtained by fitting experimental ionization energies in isoelectronic series. This reproduces the experimental Shannon-Prewitt “effective ionic radii” (for coordination number 6) with mean absolute deviation of 0.025 Å, approximately the accuracy of the experimental data itself. The remarkable agreement suggests that the calculation of other cationic attributes might be based on similar principles

Liquid Water: From Symmetry Distortions to Diffusive Motion

Water deviates from tetrahedral symmetry on different scales, creating “defects” that are important for its dynamics. In this Account, I trace the manifestations of these distortions from the isolated molecule through gas-phase clusters to the liquid phase.Unlike the common depiction, an isolated water molecule has a nonsym-metric charge distribution: although its positive charge is localized at the hydrogens, the negative charge is smeared between the lone-pair sites. This creates a “negativity track” along which a positive charge may slide. Consequently, the most facile motion within the water dimer is a reorientation of the hydrogen-bond (HB) accepting molecule (known as an “acceptor switch”), such that the donor hydrogen switches from one lone pair to the other.Liquid water exhibits asymmetry between donor and acceptor HBs. Molecular dynamics simulations show that the water oxygens accepting HBs from the central molecule are spatially localized, whereas water hydrogens donating HBs to it are distributed along the negativity track. This asymmetry is manifested in a wider acceptor- versus donor-HB distribution. There is a higher probability for a water molecule to accept one (trigonal symmetry) or three HBs than to donate one or three HBs. A simple model can explain semiquantitatively how these distributions evolve by distorting perfectly tetrahedral water. Just two reactions are required: the dissociation of a HB between a double-donor donating to a double-acceptor, D₂···A₂, followed by a switching reaction in which a HB donor rotates its hydrogen between two double-acceptor molecules.The preponderance of D₂···A₂ dissociation events is in line with HB “anticooperativity”, whereas positive cooperativity is exhibited by conditional HB distributions: a molecule with more acceptor bonds tends to have more donor bonds and vice versa. Quantum mechanically, such an effect arises from intermolecular charge transfer, but it is observed even for fixed-charge water models. Possibly, in the liquid state this is partly a collective effect, for example, a more ordered hydration shell that enhances the probability for both acceptor and donor HBs.The activation energy for liquid water self-diffusion is considerably larger than its HB strength, pointing to the involvement of collective dynamics. The remarkable agreement between the temperature dependence of the water self-diffusion coefficient and its Debye relaxation time suggests that both share the same mechanism, likely consisting of coupled rotation and translation with collective rearrangement of the environment.The auto-correlation function of a hydrogen-bonded water molecule pair is depicted quantitatively by the solution of the diffusion equation for reversible geminate recombination, up to long times where the ubiquitous <i>t</i>^–3/2 power law prevails. From the model, one obtains the HB dissociation and formation rate coefficients and their temperature dependence. Both have a similar activation enthalpy, suggesting rapid formation of HBs with alternate partners, perhaps by the HB switching reaction involving the trigonal site.A detailed picture of how small fluctuations evolve into large-scale molecular motions in water remains elusive. Nonetheless, our results demonstrate how the plasticity of water can be traced to its asymmetric charge distribution, with duality between tetrahedral and trigonal ligation states

Protonated Water Dimer on Benzene: Standing Eigen or Crouching Zundel?

Protonated water clusters that are hydrogen-bonded to a neutral benzene molecule are a reductionist model for protons at hydrophobic surfaces, which are of fundamental importance in biological energy transduction processes. Of particular interest is the protonated water dimer (“Zundel ion”) on benzene, whose gas-phase messenger IR spectrum has been previously interpreted in terms of an asymmetric binding of the protonated water dimer to the benzene ring through a single water molecule. This “standing Eigen” isomer has a hydronium core. We have found an alternative “crouching Zundel” isomer, which attaches to the benzene ring symmetrically via both of its water molecules. When Ar-tagged, it has an IR spectrum in much better agreement with experiment than the standing Eigen isomer, particularly at the lower frequencies. These conclusions are based on static harmonic (and anharmonic) normal-mode analysis using density functional theory with various (dispersion corrected) functionals and particularly on dynamic anharmonic spectra obtained from the dipole autocorrelation functions from classical ab initio molecular dynamics with the BLYP, PBE, and B3LYP functionals. Possible implications to protons on water/organic-phase interfaces are discussed

The Hole in the Barrel: Water Exchange at the GFP Chromophore

Internal water molecules in proteins are conceivably part of the protein structure, not exchanging easily with the bulk. We present a detailed molecular dynamics study of the water molecule bound to the green fluorescent protein (GFP) chromophore that conducts its proton following photoexcitation. It readily exchanges above 310 K through a hole that forms between strands 7 and 10, due to fluctuations in the 6–7 loop. As the hole widens, rapid succession of water exchange events occur. The exiting water molecule passes three layers of atoms, constituting the binding, internal, and surface sites. Along this pathway, hydrogen bonding protein residues are replaced with water molecules. The mean squared displacement along this pathway is initially subdiffusive, becomes superdiffusive as the water traverses the protein wall in a flip-flop motion, and reverts to normal diffusion in the bulk. The residence correlation function for the bound state decays biexponentially, supporting this three-site scenario. For a favorable orientation of the Thr203 side-chain, the hole often fills with a single file of water molecules that could indeed rapidly conduct the photodissociated proton outside the protein. The activation enthalpy for its formation, 26 kJ/mol, agrees with the experimental value for a protein conformation change suggested to gate proton escape

Statistics of Language Morphology Change: From Biconsonantal Hunters to Triconsonantal Farmers

<div><p>Linguistic evolution mirrors cultural evolution, of which one of the most decisive steps was the "agricultural revolution" that occurred 11,000 years ago in W. Asia. Traditional comparative historical linguistics becomes inaccurate for time depths greater than, say, 10 kyr. Therefore it is difficult to determine whether decisive events in human prehistory have had an observable impact on human language. Here we supplement the traditional methodology with independent statistical measures showing that following the transition to agriculture, languages of W. Asia underwent a transition from biconsonantal (2c) to triconsonantal (3c) morphology. Two independent proofs for this are provided. Firstly the reconstructed Proto-Semitic fire and hunting lexicons are predominantly 2c, whereas the farming lexicon is almost exclusively 3c in structure. Secondly, while Biblical verbs show the usual Zipf exponent of about 1, their 2c subset exhibits a larger exponent. After the 2c > 3c transition, this could arise from a faster decay in the frequency of use of the less common 2c verbs. Using an established frequency-dependent word replacement rate, we calculate that the observed increase in the Zipf exponent has occurred over the 7,500 years predating Biblical Hebrew namely, starting with the transition to agriculture.</p> </div

Proton Wire Dynamics in the Green Fluorescent Protein

Inside proteins, protons move on proton wires (PWs). Starting from the highest resolution X-ray structure available, we conduct a 306 ns molecular dynamics simulation of the (A-state) wild-type (wt) green fluorescent protein (GFP) to study how its PWs change with time. We find that the PW from the chromophore via Ser205 to Glu222, observed in all X-ray structures, undergoes rapid water molecule insertion between Ser205 and Glu222. Sometimes, an alternate Ser205-bypassing PW exists. Side chain rotations of Thr203 and Ser205 play an important role in shaping the PW network in the chromophore region. Thr203, with its bulkier side chain, exhibits slower transitions between its three rotameric states. Ser205 experiences more frequent rotations, slowing down when the Thr203 methyl group is close by. The combined states of both residues affect the PW probabilities. A random walk search for PWs from the chromophore reveals several exit points to the bulk, one being a direct water wire (WW) from the chromophore to the bulk. A longer WW connects the “bottom” of the GFP barrel with a “water pool” (WP1) situated below Glu222. These two WWs were not observed in X-ray structures of wt-GFP, but their analogues have been reported in related fluorescent proteins. Surprisingly, the high-resolution X-ray structure utilized herein shows that Glu222 is protonated at low temperatures. At higher temperatures, we suggest ion pairing between anionic Glu222 and a proton hosted in WP1. Upon photoexcitation, these two recombine, while a second proton dissociates from the chromophore and either exits the protein using the short WW or migrates along the GFP-barrel axis on the long WW. This mechanism reconciles the conflicting experimental and theoretical data on proton motion within GFP

Complete Assignment of the Infrared Spectrum of the Gas-Phase Protonated Ammonia Dimer

The infrared (IR) spectrum of the ammoniated ammonium dimer is more complex than those of the larger protonated ammonia clusters due to close-lying fundamental and combination bands and possible Fermi resonances (FR). To date, the only theoretical analysis involved partial dimensionality quantum nuclear dynamic simulations, assuming a symmetric structure (<i>D</i>_3<i>d</i>) with the proton midway between the two nitrogen atoms. Here we report an extensive study of the less symmetric (<i>C</i>_3<i>v</i>) dimer, utilizing both second order vibrational perturbation theory (VPT2) and <i>ab initio</i> molecular dynamics (AIMD), from which we calculated the Fourier transform (FT) of the dipole-moment autocorrelation function (DACF). The resultant IR spectrum was assigned using FTed velocity autocorrelation functions (VACFs) of several interatomic distances and angles. At 50 K, we have been able to assign all 21 AIMD fundamentals, in reasonable agreement with MP2-based VPT2, about 30 AIMD combination bands, and a difference band. The combinations involve a wag or the NN stretch as one of the components, and appear to follow symmetry selection rules. On this basis, we suggest possible assignments of the experimental spectrum. The VACF-analysis revealed two possible FR bands, one of which is the strongest peak in the computed spectrum. Raising the temperature to 180 K eliminated the “proton transfer mode” (PTM) fundamental, and reduced the number of observed combination bands and FRs. With increasing temperature, fundamentals red-shift, and the doubly degenerate wags exhibit larger anharmonic splittings in their VACF bending spectra. We have repeated the analysis for the H₃ND⁺NH₃ isotopologue, finding that it has a simplified spectrum, with all the strong peaks being fundamentals. Experimental study of this isotopologue may thus provide a good starting point for disentangling the N₂H₇⁺ spectrum

Both Zundel and Eigen Isomers Contribute to the IR Spectrum of the Gas-Phase H₉O₄ ⁺ Cluster

The “Eigen cation”, H₃O⁺(H₂O)₃, is the most prevalent protonated water structure in the liquid phase and the most stable gas-phase isomer of the H⁺(H₂O)₄ cluster. Nevertheless, its 50 K argon predissociation vibrational spectrum contains unexplainable low frequency peak(s). We have simulated the IR spectra of 10 gas-phase H⁺(H₂O)₄ isomers, that include zero to three argon ligands, using dipole autocorrelation functions from ab initio molecular dynamics with the CP2K software. We have also tested the effect of elevated temperature and dispersion correction. The Eigen isomers describe well the high frequency portion of the spectrum but do not agree with experiment below 2000 cm^–1. Most notably, they completely lack the “proton transfer bands” observed at 1050 and 1750 cm^–1, which characterize Zundel-type (H₅O₂ ⁺) isomers. In contrast, linear isomers with a Zundel core, although not the lowest in energy, show very good agreement with experiment, particularly at low frequencies. Peak assignments made with partial velocity autocorrelation functions verify that the 1750 cm^–1 band does not originate with the Eigen isomer but is rather due to coupled proton transfer/water bend in the Zundel isomer

Both Zundel and Eigen Isomers Contribute to the IR Spectrum of the Gas-Phase H₉O₄ ⁺ Cluster

The “Eigen cation”, H₃O⁺(H₂O)₃, is the most prevalent protonated water structure in the liquid phase and the most stable gas-phase isomer of the H⁺(H₂O)₄ cluster. Nevertheless, its 50 K argon predissociation vibrational spectrum contains unexplainable low frequency peak(s). We have simulated the IR spectra of 10 gas-phase H⁺(H₂O)₄ isomers, that include zero to three argon ligands, using dipole autocorrelation functions from ab initio molecular dynamics with the CP2K software. We have also tested the effect of elevated temperature and dispersion correction. The Eigen isomers describe well the high frequency portion of the spectrum but do not agree with experiment below 2000 cm^–1. Most notably, they completely lack the “proton transfer bands” observed at 1050 and 1750 cm^–1, which characterize Zundel-type (H₅O₂ ⁺) isomers. In contrast, linear isomers with a Zundel core, although not the lowest in energy, show very good agreement with experiment, particularly at low frequencies. Peak assignments made with partial velocity autocorrelation functions verify that the 1750 cm^–1 band does not originate with the Eigen isomer but is rather due to coupled proton transfer/water bend in the Zundel isomer

Reinvestigation of the Infrared Spectrum of the Gas-Phase Protonated Water Tetramer

Gas-phase H₉O₄⁺ has been considered an archetypal Eigen cation, H₃O⁺(H₂O)₃. Yet <i>ab initio</i> molecular dynamics (AIMD) suggested that its infrared spectrum is explained by a linear-chain Zundel isomer, alone or in a mixture with the Eigen cation. Recently, hole-burning experiments suggested a single isomer, with a second-order vibrational perturbation theory (VPT2) spectrum agreeing with the Eigen cation. To resolve this discrepancy, we have extended both calculations to more advanced DFT functionals, better basis sets, and dispersion correction. For Zundel-isomers, we find VPT2 anharmonic frequencies for four low-frequency modes involving the excess proton unreliable, including the 1750 cm^–1 band that is pivotal for differentiating between Zundel and Eigen isomers. Because the analogous bands of the H₅O₂⁺ cation show little effect of anharmonicity, we utilize the harmonic frequencies for these modes. With this caveat, both AIMD and VPT2 agree on the spectrum as originating from a Zundel isomer. VPT2 also shows that both isomers have the <i>s</i>ame spectrum in the high frequency region, so that the hole burning experiments should be extended to lower frequencies