Solvation structure of a sodium chloride ion pair in water

Solvation of magnesium chloride dimer in water: The case of anionic and neutral clusters

The structures of magnesium chloride dimer-water clusters, (MgCl2)2(H2O)n-/0, were investigated with size-selected anion photoelectron spectroscopy and theoretical calculations to understand the dissolution of magnesium chloride in water. The most stable structures were confirmed by comparing vertical detachment energies (VDEs) with the experimental measurements. A dramatic drop of VDE at n = 3 has been observed in the experiment, which is in accordance with the structural change of (MgCl2)2(H2O)n-. Compared to the neutral clusters, the excess electron induces two significant phenomena in (MgCl2)2(H2O)n-. First, the planar D2h geometry can be converted into a C3v structure at n = 0, making the Mg-Cl bonds easier to be broken by water molecules. More importantly, a negative charge-transfer-to-solvent process occurs after adding three water molecules (i.e., at n = 3), which leads to an obvious deviation in the evolution of the clusters. Such electron transfer behavior was noticed at n = 1 in monomer MgCl2(H2O)n-, indicating that the dimerization between two MgCl2 molecules can make the cluster more capable of binding electron. In neutral (MgCl2)2(H2O)n, this dimerization provides more sites for the added water molecules, which can stabilize the entire cluster and maintain its initial structure. Specifically, filling the coordination number to be 6 for Mg atoms can be seen as a link between structural preferences in the dissolution of the monomers, dimers, and extended bulk-state of MgCl2. This work represents an important step forward into fully understanding the solvation of MgCl2 crystals and other multivalent salt oligomers.

Structural Versatility and Energy Difference of Salt-Water Complex NaCl(H2O) Encoded in Cryogenic Photoelectron Spectroscopy

A weakly bound complex usually has multiple structural isomers with small energy differences. The sophisticated ab initio calculations are the main workhorse for providing theoretical results of different isomers. In contrast, the experimental determination of the energy difference is very rare. We report the energy-difference measurement of a model complex: salt-water complex NaCl(H₂O). We measured the energy difference among the structural isomers of the negatively charged NaCl(H₂O) complex and the neutral counterpart using cryogenic photoelectron spectroscopy. The temperature-dependent photoelectron spectra (15-300 K) revealed that the negatively charged NaCl(H₂O) and the neutral counterpart both have three isomers. The two higher-lying isomers are 186(22) and 481(48) cm^-1, respectively, above the most stable isomer for the negatively charged and 123(10) and 1821(24) cm^-1 for the neutral. These results provide a benchmark for the development of theoretic methods of weakly bound complexes. The experimental technique demonstrated here can be employed to investigate other weakly bound complexes with multiple isomers.

Structures of (NaSCN)2(H2O)n -/0 (n = 0-7) and solvation induced ion pair separation: Gas phase anion photoelectron spectroscopy and theoretical calculations

We studied (NaSCN)₂(H₂O)_n ^- clusters in the gas phase using size-selected anion photoelectron spectroscopy. The photoelectron spectra and vertical detachment energies of (NaSCN)₂(H₂O)_n ^- (n = 0-5) were obtained in the experiment. The structures of (NaSCN)₂(H₂O)_n ^-/0 up to n = 7 were investigated with density functional theory calculations. Two series of peaks are observed in the spectra, indicating that two types of structures coexist, the high electron binding energy peaks correspond to the chain style structures, and the low electron binding energy peaks correspond to the Na-N-Na-N rhombic structures or their derivatives. For the (NaSCN)₂(H₂O)_n ^- clusters at n = 3-5, the Na-N-Na-N rhombic structures are the dominant structures, the rhombic four-membered rings start to open at n = 4, and the solvent separated ion pair (SSIP) type of structures start to appear at n = 6. For the neutral (NaSCN)₂(H₂O)_n clusters, the Na-N-Na-N rhombic isomers become the dominant starting at n = 3, and the SSIP type of structures start to appear at n = 5 and become dominant at n = 6. The structural evolution of (NaSCN)₂(H₂O)_n ^-/0 (n = 0-7) confirms the possible existence of ionic clusters such as Na(SCN)₂ ^- and Na₂(SCN)⁺ in NaSCN aqueous solutions.

Exploring the Use of Polyols, Corn, and Beet Juice for Decreasing the Freezing Point of Brine Solution for Deicing of Pavements

Deicing of pavements is essential to ensure safe and timely movement of traffic in geographical locations where snow and ice events are anticipated. State and local municipalities employ brine solution with 23.3 wt% sodium chloride (NaCl) available in the form of rock salt to deice the pavements. Unlike water, the brine solution does not freeze until the temperature falls below −21.0 °C, i.e., the freezing point of water is depressed by −21.0 °C with the addition of 23.3 wt% NaCl. The depressed freezing point of the brine solution plays a key role in deicing pavements. Unfortunately, a further increase in rock salt content does not lower the freezing point of the brine solution. In this study, different combinations of agricultural products such as polyols including sorbitol, maltitol, and mannitol in brine (23.3 wt% of NaCl in water), and NaCl-juice (corn and beet juice) were investigated to achieve freezing point depressions below −21.0 °C for potential deicing applications in extremely cold areas. Different weight fractions of polyols-brine solutions ranging from 7.14% to 27.77% were considered, and corresponding freezing points were determined. While the sorbitol-brine solution exhibited the lowest freezing point of −38.1 °C at a higher concentration, the maltitol-brine solution exhibited a freezing point of −35.6 °C at the same concentration. Based on the °Brix value, beet juice had almost three times more soluble solids and a lower freezing point compared to corn juice. Adding 23.3 wt% of NaCl in 70% corn juice lowered the freezing point up to −23.5 °C.

Comparison of the Microsolvation of CaX2 (X = F, Cl, Br, I) in Water: Size-Selected Anion Photoelectron Spectroscopy and Theoretical Calculations

To understand the microsolvation of alkaline-earth dihalides in water and provide information about the dependence of solvation processes on different halides, we investigated CaBr₂(H₂O)_n^-, CaI₂(H₂O)_n^-, and CaF₂(H₂O)_n^- (n = 0-6) clusters using size-selected anion photoelectron spectroscopy and conducted theoretical calculations on these clusters and their neutrals. The results are compared with those of CaCl₂(H₂O)_n^-/0 clusters reported previously. It is found that the vertical detachment energies (VDEs) of CaCl₂(H₂O)_n^-, CaBr₂(H₂O)_n^-, and CaI₂(H₂O)_n^- show a similar trend with increasing cluster size, while the VDEs of CaF₂(H₂O)_n^- show a different trend. The VDEs of CaF₂(H₂O)_n^- are much lower than those of CaCl₂(H₂O)_n^-, CaBr₂(H₂O)_n^-, and CaI₂(H₂O)_n^-. A detailed probing of the structures shows that a significant increase of the Ca-X distance (separation of Ca²⁺-X^- ion pair) in CaCl₂(H₂O)_n^-/0, CaBr₂(H₂O)_n^-/0, and CaI₂(H₂O)_n^-/0 clusters occurred at about n = 5. However, for CaF₂(H₂O)_n^-/0, no abrupt change of the Ca-F distance with the increasing cluster size has been observed. In CaCl₂(H₂O)₆^-/0, CaBr₂(H₂O)₆^-/0, and CaI₂(H₂O)₆^-/0, the Ca atom coordinates directly with 5 H₂O molecules. However, in CaF₂(H₂O)_n^-/0, the Ca atom coordinates directly with only 2 or 3 H₂O molecules. The similarity or differences in the structures and coordination numbers are consistent with the fact that CaCl₂, CaBr₂, and CaI₂ have similar solubility, while CaF₂ has much lower solubility.

Failure of molecular dynamics to provide appropriate structures for quantum mechanical description of the aqueous chloride ion charge-transfer-to-solvent ultraviolet spectrum

The lowest band in the charge-transfer-to-solvent ultraviolet absorption spectrum of aqueous chloride ion is studied by experiment and computation. Interestingly, the experiments indicate that at concentrations up to at least 0.25 M, where calculations indicate ion pairing to be significant, there is no notable effect of ionic strength on the spectrum. The experimental spectra are fitted to aid comparison with computations. Classical molecular dynamic simulations are carried out on dilute aqueous Cl-, Na+, and NaCl, producing radial distribution functions in reasonable agreement with experiment and, for NaCl, clear evidence of ion pairing. Clusters are extracted from the simulations for quantum mechanical excited state calculations. Accurate ab initio coupled-cluster benchmark calculations on a small number of representative clusters are carried out and used to identify and validate an efficient protocol based on time-dependent density functional theory. The latter is used to carry out quantum mechanical calculations on thousands of clusters. The resulting computed spectrum is in excellent agreement with experiment for the peak position, with little influence from ion pairing, but is in qualitative disagreement on the width, being only about half as wide. It is concluded that simulation by classical molecular dynamics fails to provide an adequate variety of structures to explain the experimental CTTS spectrum of aqueous Cl-.

Hydration breaking and chemical ordering in a levitated NaCl solution droplet beyond the metastable zone width limit: evidence for the early stage of two-step nucleation

For over two decades, NaCl nucleation from a supersaturated aqueous solution has been predicted to occur via a two-step nucleation (TSN) mechanism, i.e., two sequential events, the formation of locally dense liquid regions followed by structural ordering. However, the formation of dense liquid regions in the very early stage of TSN has never been experimentally observed. By using a state-of-the-art technique, a combination of electrostatic levitation (ESL) and in situ synchrotron X-ray and Raman scatterings, we find experimental evidence that indicates the formation of dense liquid regions in NaCl bulk solution at an unprecedentedly high level of supersaturation (S = 2.31). As supersaturation increases, evolution of ion clusters leads to chemical ordering, but no topological ordering, which is a precursor for forming the dense disordered regions of ion clusters at the early stage of TSN. Moreover, as the ion clusters proceed to evolve under highly supersaturated conditions, we observe the breakage of the water hydration structure indicating the stability limit of the dense liquid regions, and thus leading to nucleation. The evolution of solute clusters and breakage of hydration in highly supersaturated NaCl bulk solution will provide new insights into the detailed mechanism of TSN for many other aqueous solutions.

Hydration processes of barium chloride: Size-selected anion photoelectron spectroscopy and theoretical calculations of BaCl2-water clusters

In order to understand the hydration processes of BaCl₂, we investigated BaCl₂(H₂O)_n ^- (n = 0-5) clusters using size-selected anion photoelectron spectroscopy and theoretical calculations. The structures of neutral BaCl₂(H₂O)_n clusters up to n = 8 were also investigated by theoretical calculations. It is found that in BaCl₂(H₂O)_n ^-/0, the Ba-Cl distances increase very slowly with the cluster size. The hydration process is not able to induce the breaking of a Ba-Cl bond in the cluster size range (n = 0-8) studied in this work. In small BaCl₂(H₂O)_n clusters with n ≤ 5, the Ba atom has a coordination number of n + 2; however, in BaCl₂(H₂O)_6-8 clusters, the Ba atom coordinates with two Cl atoms and (n - 1) water molecules, and it has a coordination number of n + 1. Unlike the previously studied MgCl₂(H₂O)_n ^- and CaCl₂(H₂O)_n ^-, negative charge-transfer-to-solvent behavior has not been observed for BaCl₂(H₂O)_n ^-, and the excess electron of BaCl₂(H₂O)_n ^- is mainly localized on the Ba atom rather on the water molecules. No observation of Ba²⁺-Cl^- separation in current work is consistent with the lower solubility of BaCl₂ compared to MgCl₂ and CaCl₂. Considering the BaCl₂/H₂O mole ratio in the saturated solution, one would expect that about 20-30 H₂O molecules are needed to break the first Ba-Cl bond in BaCl₂.

Combined influence of ectoine and salt: spectroscopic and numerical evidence for compensating effects on aqueous solutions

Ectoine is an important osmolyte, which allows microorganisms to survive in extreme environmental salinity. The hygroscopic effects of ectoine in pure water can be explained by a strong water binding behavior whereas a study on the effects of ectoine in salty solution is yet missing. We provide Raman spectroscopic evidence that the influence of ectoine and NaCl are opposing and completely independent of each other. The effect can be explained by the formation of strongly hydrogen-bonded water molecules around ectoine which compensate the influence of the salt on the water dynamics. The mechanism is corroborated by first principles calculations and broadens our understanding of zwitterionic osmolytes in aqueous solution. Our findings allow us to provide a possible explanation for the relatively high osmolyte concentrations in halotolerant bacteria.

Nonexponential kinetics of ion pair dissociation in electrofreezing water

Temporally- or spatially-heterogeneous environments can participate in many kinetic processes, from chemical reactions and self-assembly to the forced dissociation of biomolecules. Here, we simulate the molecular dynamics of a model ion pair forced to dissociate in an explicit, aqueous solution. Triggering dissociation with an external electric field causes the surrounding water to electrofreeze and the ion pair population to decay nonexponentially. To further probe the role of the aqueous environment in the kinetics, we also simulate dissociation events under a purely mechanical force on the ion pair. In this case, regardless of whether the surrounding water is a liquid or already electrofrozen, the ion pair population decays exponentially with a well-defined rate constant that is specific to the medium and applied force. These simulation data, and the rate parameters we extract, suggest the disordered kinetics in an electrofreezing medium are a result of the comparable time scales of two concurrent processes, electrofreezing and dissociation.

Microscopic dynamics of charge separation at the aqueous electrochemical interface

We have used molecular simulation and methods of importance sampling to study the thermodynamics and kinetics of ionic charge separation at a liquid water-metal interface. We have considered this process using canonical examples of two different classes of ions: a simple alkali-halide pair, Na⁺I^-, or classical ions, and the products of water autoionization, H₃O⁺OH^-, or water ions. We find that for both ion classes, the microscopic mechanism of charge separation, including water's collective role in the process, is conserved between the bulk liquid and the electrode interface. However, the thermodynamic and kinetic details of the process differ between these two environments in a way that depends on ion type. In the case of the classical ion pairs, a higher free-energy barrier to charge separation and a smaller flux over that barrier at the interface result in a rate of dissociation that is 40 times slower relative to the bulk. For water ions, a slightly higher free-energy barrier is offset by a higher flux over the barrier from longer lived hydrogen-bonding patterns at the interface, resulting in a rate of association that is similar both at and away from the interface. We find that these differences in rates and stabilities of charge separation are due to the altered ability of water to solvate and reorganize in the vicinity of the metal interface.

Emergence of Solvent-Separated Na+-Cl- Ion Pair in Salt Water: Photoelectron Spectroscopy and Theoretical Calculations

Solvation of salts in water is a fundamental physical chemical process, but the underlying mechanism remains unclear. We investigated the contact ion pair (CIP) to solvent-separated ion pair (SSIP) transition in NaCl(H₂O)_n clusters with anion photoelectron spectroscopy and ab initio calculations. It is found that the SSIP type of structures show up at n = 2 for NaCl^-(H₂O)_n anions. For neutral NaCl(H₂O)_n, the CIP structures are dominant at n < 9. At n = 9-12, the CIP structures and SSIP structures of NaCl(H₂O)_n are nearly degenerate in energy, coincident to the H₂O:NaCl molar ratio of NaCl saturated solution and implying that the CIP and SSIP structures can coexist in concentrated solutions. These results are useful for understanding the solvation of salts at the molecular level.

On the dissolution of lithium sulfate in water: anion photoelectron spectroscopy and density functional theory calculations

The initial dissolution steps of lithium sulfate (Li2SO4) in water were investigated by performing anion photoelectron spectroscopy and density functional theory calculations on the Li2SO4(H2O)n(-) (n = 0-5) clusters. The plausible structures of these clusters and the corresponding neutral clusters were obtained using LC-ωPBE/6-311++G(d,p) calculations by comparing the experimental and theoretical vertical electron detachment energies. Two types of structures for bare Li2SO4(-/0) were found: a turtle-shaped structure and a propeller-shaped structure. For Li2SO4(H2O)n(-) cluster anions with n = 1-3, two kinds of isomers derived from the turtle-shaped and propeller-shaped structures of bare Li2SO4(-) were identified. For n = 4-5, these two kinds of isomers present similar structural and energetic features and thus are not distinguishable. For the anionic clusters the water molecules prefer to firstly interact with one Li atom until fully coordinating it. While for the neutral clusters, the water molecules interact with the two Li atoms alternately, therefore, showing a pairwise solvation behavior. The Li-S distance increases smoothly upon addition of water molecules one by one. Addition of five water molecules to Li2SO4 cannot induce the dissociation of one Li(+) ion because the water molecules are shared by two Li(+) ions.

A comparative study of the effects of the Hofmeister series anions of the ionic salts and ionic liquids on the stability of α-chymotrypsin

Direct interactions between the anion and the catalytic amino acid residues lead to denaturation of CT.

Solvation effects on like-charge attraction

We present results of molecular dynamics simulations of the electrostatic interaction between two parallel charged rods in the presence of divalent counterions. Such polyelectrolytes have been considered as a simple model for understanding electrostatic interactions in highly charged biomolecules such as DNA. Since there are correlations between the free charge carriers, the phenomenon of like charge attraction appears for specific parameters. We explore the role of solvation effects and the resulting deviations from Coulomb's law on the nanoscale on this peculiar phenomenon. The behavior of the force between the charged rods in a simulation with atomistic representation of water molecules is completely different from a model in which water is modeled as a continuum dielectric. By calculating counterion-rodion pair correlation functions, we find that the presence of water molecules changes the structure of the counterion cloud and results in both qualitative and quantitative changes of the force between highly charged polyelectrolytes.

Dissolution kinetics and mechanisms at dolomite-water interfaces: effects of electrolyte specific ionic strength

Elucidating dissolution kinetics and mechanisms at carbonate mineral-water interfaces is essential to many environmental and geochemical processes, including geologic CO(2) sequestration in deep aquifers. In the present work, effects of background electrolytes on dolomite (CaMg(CO(3))(2)) reactivity were investigated by measuring step dissolution rates using in situ hydrothermal atomic force microscopy (HAFM) at 90 °C. Cleaved surfaces of dolomite were exposed to sodium chloride and tetramethylammonium chloride (TMACl) aqueous solutions with ionic strengths (I) ranging from 0 to 0.77 m at pH 4 and pH 9. HAFM results demonstrated that dolomite step retreat rates increased with increasing solution ionic strength and decreasing pH. Comparison of [481] and [441] steps revealed that the anisotropy of [481] and [441] step speeds became significant as solution ionic strength increased, with NaCl exerting more pronounced effects than TMACl for the same I. To interpret the different trends observed for NaCl and TMACl, a dissolution mechanism involving orientation-dependent ion adsorption and consequent edge free energy changes is proposed.

Toward the mechanism of ionic dissociation in water

We investigate the solvent effects leading to dissociation of sodium chloride in water. Thermodynamic analysis reveals dissociation to be driven energetically and opposed entropically, with the loss in entropy due to an increasing number of solvent molecules entering the highly coordinated ionic solvation shell. We show through committor analysis that the ion–ion distance is an insufficient reaction coordinate, in agreement with previous findings. By application of committor analysis on various constrained solvent ensembles, we find that the dissociation event is generally sensitive to solvent fluctuations at long ranges, with both sterics and electrostatics of importance. The dynamics of the reaction reveal that solvent rearrangements leading to dissociation occur on time scales from 0.5 to 5 ps or longer, and that, near the transition state, inertial effects enhance the reaction probability of a given trajectory.

SIZE DEPENDENCE OF SOLVATION STRUCTURE AND DYNAMICS OF IONS IN LIQUID N-METHYLACETAMIDE: A MOLECULAR DYNAMICS SIMULATION STUDY

The solvation structure and dynamics of alkali metal (Li+, Na+, K+, Rb+, Cs+) and halide (F-, Cl-, Br-, I-) ions in liquid N -methylacetamide (NMA) are calculated at two different temperatures T = 313 K and 453 K, by using classical molecular dynamics simulations. We have also considered [Formula: see text] and some larger cations such as I +, Me 4 N +, and Et4N+ in this study to investigate the size dependence solvation structure and dynamics of ions in liquid NMA. With the increase of ion size, the self-diffusion coefficients of cations are found to increase and the maximum is observed at Me4N+ , whereas for halide ions the increase of diffusion coefficient with ion size continues up to I- and no maximum is observed. However, the relative increase of the diffusion coefficients of larger ion compared to those of Li+ and F+ are found to be significantly higher at low temperature. Results are very good in agreement with experimental observation.

Hydration-determined orientational preferences in aromatic association from benzene dimer free energy volumes

In this study of the thermodynamics of benzene association in water, we show that although the potential energy and enthalpy play an important role in the association of benzene dimers, they do not determine the relative orientation of these molecules on close contact in solution. We observe a large variation in the configurations that contribute to the vacuum (i.e., solvent-free) minimum free energy wells of the benzene contact pair. In water, fewer and smaller minimum free energy wells are observed. On examination, we find that fewer close contact configurations of benzene dimers populate these wells and that they are more energetically distinct from each other (compared with the vacuum case). The edge-over-edge configuration is most likely in solution and appears to evolve from the entropically favored side-by-side solvent shared configuration. Therefore, the relative orientation of the benzene molecules (i.e., parallel displaced, T-shaped, etc.) on association is a result of maximizing the contribution of the benzene-benzene entropy of association, to the solution free energy.

Computing free energy hypersurfaces for anisotropic intermolecular associations

We previously used an adaptive reaction coordinate force biasing method for calculating the free energy of conformation (Naidoo and Brady, J Am Chem Soc 1999, 121, 2244) and chemical reactions (Rajamani et al., J Comput Chem 2003, 24, 1775) amongst others. Here, we describe a generalized version able to produce free energies in multiple dimensions, descriptively named the free energies from adaptive reaction coordinate forces method. To illustrate it, we describe how we calculate a multidimensional intermolecular orientational free energy, which can be used to investigate complex systems such as protein conformation and liquids. This multidimensional intermolecular free energy W(r, theta(1), theta(2), phi) provides a measure of orientationally dependent interactions that are appropriate for applications in systems that inherently have molecular anisotropic features. It is a highly informative free energy volume, which can be used to parameterize key terms such as the Gay-Berne intermolecular potential in coarse grain simulations. To demonstrate the value of the information gained from the W(r, theta(1), theta(2), phi) hypersurfaces we calculated them for TIP3P, TIP4P, and TIP5P dimer water models in vacuum. A comparison with a commonly used one-dimensional distance free energy profile is made to illustrate the significant increase in configurational information. The W(r) plots show little difference between the three models while the W(r, theta(1), theta(2), phi) hypersurfaces reveal the underlying energetic reasons why these potentials reproduce tetrahedrality in the condensed phase so differently from each.

Coarse-grained ions without charges: reproducing the solvation structure of NaCl in water using short-ranged potentials

A coarse-grained model of NaCl in water is presented where the ions are modeled without charge to avoid computationally challenging electrostatics. A monatomic model of water [V. Molinero and E. B. Moore, J. Phys. Chem. B 113, 4008 (2009)] is used as the basis for this coarse-grain approach. The ability of Na(+) to disrupt the native tetrahedral arrangement of water molecules, and of Cl(-) to integrate within this organization, is preserved in this mW-ion model through parametrization focused on water's solvation of these ions. This model successfully reproduces the structural effect of ions on water, referenced to observations from experiments and atomistic molecular dynamics simulations, while using extremely short-ranged potentials. Without Coulomb interactions the model replicates details of the ion-water structure such as distinguishing contact and solvent-separated ion pairs and the free energy barriers between them. The approach of mimicking ionic effects with short-ranged interactions results in performance gains of two orders of magnitude compared to Ewald methods. Explored over a broad range of salt concentration, the model reproduces the solvation structure and trends of diffusion relative to atomistic simulations and experimental results. The functional form of the mW-ion model can be parametrized to represent other electrolytes. With increased computational efficiency and reliable structural fidelity, this model promises to be an asset for accessing significantly longer simulation time scales with an explicit solvent in a coarse-grained system involving, for example, polyelectrolytes such as proteins, nucleic acids, and fuel-cell membranes.

Computing accurate potentials of mean force in electrolyte solutions with the generalized gradient-augmented harmonic Fourier beads method

We establish the accuracy of the novel generalized gradient-augmented harmonic Fourier beads (ggaHFB) method in computing free-energy profiles or potentials of mean force (PMFs) through comparison with two independent conventional techniques. In particular, we employ umbrella sampling with one dimensional weighted histogram analysis method (WHAM) and free molecular dynamics simulation of radial distribution functions to compute the PMF for the Na(+)-Cl(-) ion-pair separation to 16 A in 1.0M NaCl solution in water. The corresponding ggaHFB free-energy profile in six dimensional Cartesian space is in excellent agreement with the conventional benchmarks. We then explore changes in the PMF in response to lowering the NaCl concentration to physiological 0.3 and 0.1M, and dilute 0.0M concentrations. Finally, to expand the scope of the ggaHFB method, we formally develop the free-energy gradient approximation in arbitrary nonlinear coordinates. This formal development underscores the importance of the logarithmic Jacobian correction to reconstruct true PMFs from umbrella sampling simulations with either WHAM or ggaHFB techniques when nonlinear coordinate restraints are used with Cartesian propagators. The ability to employ nonlinear coordinates and high accuracy of the computed free-energy profiles further advocate the use of the ggaHFB method in studies of rare events in complex systems.

Molecular Engineering of Intensely Near-Infrared Absorbing Excited States in Highly Conjugated Oligo(porphinato)zinc−(Polypyridyl)metal(II) Supermolecules

A new series of chromophores, MPZn(n), which combine ethyne-bridged bis(terpyridyl)metal(II)-(porphinato)zinc(II) (MPZ(n)) and oligomeric, ethyne-bridged (porphinato)zinc(II) (PZn(n)) architectures, have been synthesized and characterized, along with a series of derivatives bearing pyrrolidinyl electron-releasing groups on the ancillary terpyridine units (Pyr(m)MPZn(n)). Cyclic voltammetric studies, as well as NMR, electronic absorption, fluorescence, and femtosecond pump-probe transient absorption spectroscopies, have been employed to study the ground- and excited-state properties of these unusual chromophores. All of these species possess intensely absorbing excited states having large spectral bandwidth that penetrate deep in the near-infrared (NIR) energy regime. Electronic structural variation of the molecular framework shows that the excited-state absorption maximum can be extensively modulated [lambdamax(T(1) --> T(n))] (880 nm < lambdamax < 1126 nm), while concomitantly maintaining impressively large T(1) --> T(n) absorption manifold spectral bandwidth (full width at half-maximum, fwhm, approximately 2000-2500 cm(-1)). Furthermore, these studies enable correlation of supermolecular electronic structure with the magnitude of the excited-state lifetime (tau(es)) and demonstrate that this parameter can be modulated over 4 orders of magnitude ( approximately 1 ns < tau(es) < 45 micros). Terpyridyl pyrrolidinyl substituents can be utilized to destabilize terpyridyl ligand pi(*) energy levels and diminish the E1/2 (M3+/2+) value of the bis(terpyridyl)metal(II) center: such perturbations determine the relative energies of the PZn(n)-derived 1pi-pi(*) and bis(terpyridyl)metal(II) charge-transfer states and establish whether the T(1)-state wave functions of MPZn(n) and PyrmMPZn(n) species manifest the extensive electronic delocalization and charge-separated (CS) features characteristic of long-lived triplet states that absorb strongly in the NIR.

A comparison of methods to compute the potential of mean force

Most processes occurring in a system are determined by the relative free energy between two or more states because the free energy is a measure of the probability of finding the system in a given state. When the two states of interest are connected by a pathway, usually called reaction coordinate, along which the free-energy profile is determined, this profile or potential of mean force (PMF) will also yield the relative free energy of the two states. Twelve different methods to compute a PMF are reviewed and compared, with regard to their precision, for a system consisting of a pair of methane molecules in aqueous solution. We analyze all combinations of the type of sampling (unbiased, umbrella-biased or constraint-biased), how to compute free energies (from density of states or force averaging) and the type of coordinate system (internal or Cartesian) used for the PMF degree of freedom. The method of choice is constraint-bias simulation combined with force averaging for either an internal or a Cartesian PMF degree of freedom.