Lateral diffusion of ions near membrane surface.

Biological membranes isolate living cells from their environment, while allowing selective molecular transport between the inner and outer realms. For example, Na+ and K+ permeability through ionic channels contributes to neural conduction. Whether the ionic currents arise directly from cations in the bulk, or from the interface, is currently unclear. There are only scant results concerning lateral diffusion of ions on aquated membrane surfaces (and strong belief that this occurs through binding to a diffusing lipid). We performed classical molecular dynamics (MD) simulations of monovalent ions, Na+, K+, and Cl-, near the surface of the zwitterionic palmitoyl-oleoyl-phosphatidylcholine (POPC) membrane. Realistic force-fields for lipids (Amber's Lipid17 and Lipid21) and water (TIP4P-Ew) are tested for the mass and charge densities and the electrostatic potential across the membrane. These calculations reveal that the chloride can bind to the choline moiety through an intervening water molecule by forming a CH⋯OH hydrogen bond, while cations bind to both the phosphatic and carbonyl oxygens of phosphatidylcholine moieties. Upon transitioning from the bulk to the interface, a cation sheds some of its hydration water, which are replaced by headgroup atoms. Notably, an interfacial cation can bind 1-4 headgroup atoms, which is a key to understanding its surface hopping mechanism. We find that cation binding to three headgroup atoms immobilizes it, while binding to four energizes it. Consequently, the lateral cation diffusion rate is only 15-25 times slower than in the bulk, and 4-5 times faster than lipid self-diffusion. K+ diffusion is notably more anomalous than Na+, switching from sub- to super-diffusion after about 2 ns.

Temperature and Nuclear Quantum Effects on the Stretching Modes of the Water Hexamer.

The water hexamer has many low-lying isomers, e.g., ring, book, cage, and prism, shifting from two- to three-dimensional structures. We show that this dimensionality change is accompanied by a drop in the quantum nature of the cluster, as manifested in the red shift of the quantal OH stretching modes as compared with their classical counterparts. We obtain this "nuclear quantum effect" (NQE) as the mean deviation between the OH stretch frequencies from velocity autocorrelation Fourier transforms from classical trajectories on a high-level water potential (MB-pol) as compared with scaled harmonic frequencies from high-level quantum chemistry calculations. With a universal scaling factor, the predicted OH frequencies agree with experiment to a mean absolute deviation ≤10 cm-1, which allows unequivocal isomer assignments. By assuming temperature-independent NQEs, we produce the temperature dependence of the cage isomer OH stretch spectrum below 70 K, where it is the dominant structure. All bands widen and blue-shift with increasing temperature, most conspicuously the reddest mode, which thus constitutes a "vibrational thermometer".

Ionic radii of hydrated sodium cation from QTAIM.

The sodium cation is ubiquitous in aqueous chemistry and biological systems. Yet, in spite of numerous studies, the (average) distance between the sodium cation and its water ligands, and the corresponding ionic radii, are still controversial. Recent experimental values in solution are notably smaller than those from previous X-ray studies and ab initio molecular dynamics. Here we adopt a "bottom-up" approach of obtaining these distances from quantum chemistry calculations [full MP2 with the 6-31++G(d,p) and cc-pVTZ basis-sets] of gas-phase Na+(H2O)n clusters, as a function of the sodium coordination number (CN = 2-6). The bulk limit is obtained by the polarizable continuum model, which acts to increase the interatomic distances at small CN, but has a diminishing effect as the CN increases. This extends the CN dependence of the sodium-water distances from crystal structures (CN = 4-12) to lower CN values, revealing a switch between two power laws, having a small exponent at small CNs and a larger one at large CNs. We utilize Bader's theory of atoms in molecules to bisect the Na+-O distances into Na+ and water radii. Contrary to common wisdom, the water radius is not constant, decreasing even more than that of Na+ as the CN decreases. We also find that the electron density at the bond critical point increases exponentially as the sodium radius decreases.

Protons and Hydroxide Ions in Aqueous Systems.

Understanding the structure and dynamics of water's constituent ions, proton and hydroxide, has been a subject of numerous experimental and theoretical studies over the last century. Besides their obvious importance in acid-base chemistry, these ions play an important role in numerous applications ranging from enzyme catalysis to environmental chemistry. Despite a long history of research, many fundamental issues regarding their properties continue to be an active area of research. Here, we provide a review of the experimental and theoretical advances made in the last several decades in understanding the structure, dynamics, and transport of the proton and hydroxide ions in different aqueous environments, ranging from water clusters to the bulk liquid and its interfaces with hydrophobic surfaces. The propensity of these ions to accumulate at hydrophobic surfaces has been a subject of intense debate, and we highlight the open issues and challenges in this area. Biological applications reviewed include proton transport along the hydration layer of various membranes and through channel proteins, problems that are at the core of cellular bioenergetics.

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 (S) and effective principal quantum number (n*) 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.

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 ab initio 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 same spectrum in the high frequency region, so that the hole burning experiments should be extended to lower frequencies.

Structure, spectroscopy, and dynamics of the phenol-(water)2 cluster at low and high temperatures.

Aqueous solutions are complex due to hydrogen bonding (HBing). While gas-phase clusters could provide clues on the solution behavior, most neutral clusters were studied at cryogenic temperatures. Recent results of Shimamori and Fujii provide the first IR spectrum of warm phenol-(H2O)2 clusters. To understand the temperature (T) effect, we have revisited the structure and spectroscopy of phenol-(H2O)2 at all T. While older quantum chemistry work concluded that the cyclic isomers are the most stable, the inclusion of dispersion interactions reveals that they are nearly isoenergetic with isomers forming π-HBs with the phenyl ring. Whereas the OH-stretch bands were previously assigned to purely local modes, we show that at low T they involve a concerted component. We have calculated the (static) anharmonic IR spectra for all low-lying isomers, showing that at the MP2 level, one can single out one isomer (udu) as accounting for the low-T spectrum to 3 cm-1 accuracy. Yet no isomer can explain the substantial blueshift of the phenyl-OH band at elevated temperatures. We describe the temperature effect using ab initio molecular dynamics with a density functional and basis-set (B3LYP-D3/aug-cc-pVTZ) that provide a realistic description of OH⋯O vs. OH⋯π HBing. From the dipole moment autocorrelation function, we obtain good description for both low- and high-T spectra. Trajectory visualization suggests that the ring structure remains mostly intact even at high T, with intermittent switching between OH⋯O and OH⋯π HBing and lengthening of all 3 HBs. The phenyl-OH blueshift is thus attributed to strengthening of its OH bond. A model for three beads on a ring suggests that this shift is partly offset by the elimination of coupling to the other OH bonds in the ring, whereas for the two water molecules these two effects nearly cancel.

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 (D3d) with the proton midway between the two nitrogen atoms. Here we report an extensive study of the less symmetric (C3v) dimer, utilizing both second order vibrational perturbation theory (VPT2) and ab initio 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.

Deciphering the infrared spectrum of the protonated water pentamer and the hybrid Eigen-Zundel cation.

Traditionally, infrared band assignment for the protonated water clusters, such as H(+)(H2O)5, is based on their lowest energy isomer. Recent experiments extend the observation spectral window to lower frequencies, for which such assignment appears to be inadequate. Because this hydrogen-bonded system is highly anharmonic, harmonic spectral calculations are insufficient for reliable interpretation. Consequently, we have calculated the IR spectrum of several isomers of the protonated water pentamer using an inherently anharmonic methodology, utilizing dipole and velocity autocorrelation functions computed from ab initio molecular dynamic trajectories. While the spectrum of H(+)(H2O)5 is universally assumed to represent the branched Eigen isomer, we find a better agreement for a mixture of a ring and linear isomers. The first has an Eigen core and contributes at high frequencies, whereas the latter accounts for all prominent low-frequency bands. Interestingly, its core is neither a classical Eigen nor a Zundel cation, but rather has hybrid geometry. Such an isomer may play a role in proton conductance along short proton wires.

Network analysis of proton transfer in liquid water.

Proton transfer in macromolecular systems is a fascinating yet elusive process. In the last ten years, molecular simulations have shown to be a useful tool to unveil the atomistic mechanism. Notwithstanding, the large number of degrees of freedom involved make the accurate description of the process very hard even for the case of proton diffusion in bulk water. Here, multi-state empirical valence bond molecular dynamics simulations in conjunction with complex network analysis are applied to study proton transfer in liquid water. Making use of a transition network formalism, this approach takes into account the time evolution of several coordinates simultaneously. Our results provide evidence for a strong dependence of proton transfer on the length of the hydrogen bond solvating the Zundel complex, with proton transfer enhancement as shorter bonds are formed at the acceptor site. We identify six major states (nodes) on the network leading from the "special pair" to a more symmetric Zundel complex required for transferring the proton. Moreover, the second solvation shell specifically rearranges to promote the transfer, reiterating the idea that solvation beyond the first shell of the Zundel complex plays a crucial role in the process.

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 nonsymmetric 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, D(2)···A(2), followed by a switching reaction in which a HB donor rotates its hydrogen between two double-acceptor molecules. The preponderance of D(2)···A(2) 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 t(-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.

Collagen Structured Hydration.

Collagen is a triple-helical protein unique to the extracellular matrix, conferring rigidity and stability to tissues such as bone and tendon. For the [(PPG)10]3 collagen-mimetic peptide at room temperature, our molecular dynamics simulations show that these properties result in a remarkably ordered first hydration layer of water molecules hydrogen bonded to the backbone carbonyl (bb-CO) oxygen atoms. This originates from the following observations. The radius of gyration attests that the PPG triplets are organized along a straight line, so that all triplets (excepting the ends) are equivalent. The solvent-accessible surface area (SASA) for the bb-CO oxygens shows a repetitive regularity for every triplet. This leads to water occupancy of the bb-CO sites following a similar regularity. In the crystal-phase X-ray data, as well as in our 100 K simulations, we observe a 0-2-1 water occupancy in the P-P-G triplet. Surprisingly, a similar (0-1.7-1) regularity is maintained in the liquid phase, in spite of the sub-nsec water exchange rates, because the bb-CO sites rarely remain vacant. The manifested ordered first-shell water molecules are expected to produce a cylindrical electrostatic potential around the peptide, to be investigated in future work.

Green's function for reversible geminate reaction with volume reactivity.

The kinetics of a diffusing particle near a reversible trap may be described by an extension of the Feynman-Kac equation to the case of reversible binding, which can occur within a finite reaction sphere. We obtain the Green's function solution for the Laplace transform of this equation when the particle is initially either bound or unbound. We study the solution in the time-domain by either inverting the Laplace transform numerically or propagating the partial differential equation in the time-domain. We show that integrals of this solution over the reaction sphere agree with previously obtained solutions.

The residence probability: single molecule fluorescence correlation spectroscopy and reversible geminate recombination.

The residence probability of a freely diffusing particle within an open d-dimensional ball is calculated as a function of time, for an initial distribution that is either a spherical delta function or uniform within the sphere. The latter is equivalent to the autocorrelation function (ACF) of fluorescence correlation spectroscopy (FCS) when utilizing near-field scanning optical microscopy (NSOM) probes. Starting from the general equation for the Laplace transform of the residence probability, we solve it in Laplace space for any dimensionality, inverting it into the time domain in one- and three-dimensions. The short- and long-time asymptotic behaviors of the residence probability are derived and compared with the exact results. Approximations for the two-dimensional ACF are discussed, and a new approximation is derived for the NSOM-FCS ACF. Also of interest is an analytic expression for a three-dimensional ACF, which could be useful for two-photon FCS. Analogy with the binding probability for reversible geminate recombination suggests that more information could be extracted from the long-time tails in FCS experiments.

Single molecule diffusion and the solution of the spherically symmetric residence time equation.

The residence time of a single dye molecule diffusing within a laser spot is propotional to the total number of photons emitted by it. With this application in mind, we solve the spherically symmetric "residence time equation" (RTE) to obtain the solution for the Laplace transform of the mean residence time (MRT) within a d-dimensional ball, as a function of the initial location of the particle and the observation time. The solutions for initial conditions of potential experimental interest, starting in the center, on the surface or uniformly within the ball, are explicitly presented. Special cases for dimensions 1, 2, and 3 are obtained, which can be Laplace inverted analytically for d = 1 and 3. In addition, the analytic short- and long-time asymptotic behaviors of the MRT are derived and compared with the exact solutions for d = 1, 2, and 3. As a demonstration of the simplification afforded by the RTE, the Appendix obtains the residence time distribution by solving the Feynman-Kac equation, from which the MRT is obtained by differentiation. Single-molecule diffusion experiments could be devised to test the results for the MRT presented in this work.

Visualizing proton antenna in a high-resolution green fluorescent protein structure.

"Proton-collecting antenna" are conjectured to consist of several carboxylates within hydrogen-bond (HB) networks on the surface of proteins, which funnel protons to the orifice of an internal proton wire leading to the protein's active site. Yet such constructions were never directly visualized. Here we report an X-ray structure of green fluorescent protein (GFP) of the highest resolution to date (0.9 A). It allows the identification of some pivotal hydrogen atoms pertinent to uncertainties concerning the protonation state of the chromophore. Applying a computer algorithm for mapping proton wires in proteins reveals the previously observed "active site wire" connecting Glu222 with the surface carboxylate Glu5. In addition, it is now possible to identify what appears to be a proton-collecting apparatus of GFP. It consists of a negative surface patch containing carboxylates, threonines, and water molecules, connected by a HB network to Glu5. Furthermore, we detect exit points via Asn146 and His148 to a hydrophobic surface region. The more extensive HB network of the present structure, as compared with earlier GFP structures, is not accidental. A systematic investigation of over 100 mutants shows a clear correlation between the observed water content of GFP X-ray structures and their resolution. With increasing water content, the proton wires become progressively larger. These findings corroborate the scenario in which the photodissociated proton from wild-type GFP can leak outside, whereafter another proton is recruited via the proton-collecting apparatus reported herein.

Mapping proton wires in proteins: carbonic anhydrase and GFP chromophore biosynthesis.

We have developed an algorithm for mapping proton wires in proteins and applied it to the X-ray structures of human carbonic anhydrase II (CA-II), the green fluorescent protein (GFP), and some of their mutants. For both proteins, we find more extensive proton wires than typically reported. In CA-II the active site wire exits to the protein surface, and leads to Glu69 and Asp72, located on an electronegative patch on the rim of the active site cavity. One possible interpretation of this observation is that positively charged, protonated buffer molecules dock in that area, from which a proton is delivered to the active site when the enzyme works in the dehydration direction. In GFP we find a new internal proton wire, in addition to the previously reported wire involved in excited state proton transfer. The new wire is located on the other face of the chromophore, and we conjecture that it plays a role in chromophore biosynthesis that occurs following protein folding. In the last step of this process, transient carbanion formation was suggested to occur on the bridge carbon [Pouwels et al. Biochemistry 2008, 47, 10111]. Residues on the new wire (Thr62, His181, Arg96) may participate in proton abstraction from this bridge carbon atom. A possible mechanism involves a rotation of the Thr62 side chain and completion of a short wire by which the proton is transported to His181, while the negative charge is transferred to the imidazolone carbonyl, producing a homoenolate intermediate that is stabilized by Arg96. Finally, comparison of the proton wires in the two proteins reveals common motifs, such as short internalized Ser/Thr-Glu hydrogen-bonded pairs for ultrafast proton abstraction, and threonine side chain rotation functioning as a proton wire switch.

Distance-dependent proton transfer along water wires connecting acid-base pairs.

We report time-resolved mid-IR kinetics for the ultrafast acid-base reaction between photoexcited 8-hydroxypyrene-1,3,6-trisulfonic acid trisodium salt (HPTS), and acetate at three concentrations (0.5, 1.0, and 2.0 M) and three temperatures (5, 30, and 65 degrees C) in liquid D(2)O. The observed proton-transfer kinetics agree quantitatively, over all times (200 fs-500 ps), with an extended Smoluchowski model which includes distance-dependent reactivity in the form of a Gaussian rate function, k(r). This distance dependence contrasts with the exponential k(r) that is typically observed for electron-transfer reactions. The width of k(r) is essentially the only parameter varied in fitting the proton-transfer kinetics at each concentration and temperature. We find that k(r) likely represents the rate of concerted (multi)proton hopping across "proton wires" of different length r that connect acid-base pairs in solution. The concerted nature of the proton transfer is supported by the fact that k(r) shows a steeper dependence on r at higher temperatures.

Multisite reversible geminate reaction.

We provide an analytic solution for diffusion-influenced geminate reaction with multiple (N) reversible binding sites (of which one may be irreversible). The solution obtained in the Laplace domain, for two different initial conditions, is valid for the case when the sites are overlapping spheres with no long-range interactions with the diffusing particle. The possibility to invert into the time domain is determined by a characteristic polynomial. When all its roots are distinct, it is possible to apply the Lagrange interpolation formula and obtain a partial-fraction expansion that can be termwise inverted. At long times the occupancy of all sites, and for all initial conditions, decays as t(-3/2). The behavior at short times depends on the initial condition: when starting from contact, the binding probability rises as t(1/2), but if the particle is initially bound to one of the sites, the occupancy of the others rises as t(3/2). In between these two power laws we observe an intermediate-time kinetics consisting of N decaying exponentials. Those which are slower than a characteristic diffusion time are in the reaction-control regime and fit a discrete-state kinetic approximation with no adjustable parameters, whereas the faster kinetic steps are diffusion controlled. The model solved herein may depict a wide range of physical situations, from multisite proton transfer kinetics to hydrogen-bond dynamics of liquid water.

Temperature Dependence of Intramolecular Vibrational Bands in Small Water Clusters.

Cyclic water clusters are pivotal for understanding atmospheric reactions as well as liquid water, yet the temperature (T) dependence of their dynamics and spectroscopy is poorly studied. The development of highly accurate water potentials, such as MB-pol, partly rectifies this. It remains to account for the quantum nuclear effects (NQE), because quantum nuclear dynamics become increasingly inaccurate at low temperatures. From a practical point of view, we find that NQE can be accounted for simply by subtracting a constant from the frequencies obtained from the velocity autocorrelation functions (VACF) of classical nuclear dynamics, resulting in unprecedented agreement with experiment, mostly within 5 cm-1. We have performed classical simulations of (H2O)n clusters (n = 2-5) from 20 K and up to their melting temperature, calculating both all-atom and partial VACF, thus generating the temperature dependence of the vibrational frequencies (IR and Raman bands). Focusing on the hydrogen-bonded (HBed) OH stretch and HOH bend, we find opposing T dependencies. The HBed OH modes blue shift linearly with T, attributed to ring expansion rather than any specific conformational change. The lowest-frequency Raman concerted mode is predicted to show the largest such shift. In contrast, the HOH bend undergoes a red-shift, with the highest frequency concerted band undergoing the largest red-shift. These results can be explained by a coupled-oscillator model for n hydrogen atoms on a ring, constrained to move either tangentially (stretch) or perpendicularly (bend) to the ring. With increasing temperature and weakening of HBs, the intrinsic force constant increases (stretch) or remains constant (bend), while the nearest-neighbor coupling constant decreases, and this results in the interesting behavior revealed herein. T-dependent Raman studies are required for testing some of these predictions.