Nonlinear Free Energy Relations for Adiabatic Proton Transfer Reactions in a Polar Environment. II. Inclusion of the Hydrogen Bond Vibration

Elementary Reaction Steps That Precede or Follow a Unimolecular Reaction Step Can Obfuscate Interpretation of the Driving-Force Dependence to Its Rate Constant

Assessing the validity of a driving-force-dependent kinetic theory for a unimolecular elementary reaction step is difficult when the observed reaction rate is strongly influenced by properties of the preceding or following elementary reaction step. A well-known example occurs for bimolecular reactions with weak orbital overlap, such as outer-sphere electron transfer, where bimolecular collisional encounters that precede a fast unimolecular electron-transfer step can limit the observed rate. A lesser-appreciated example occurs for bimolecular reactions with stronger orbital overlap, including many proton-transfer reactions, where equilibration of an endergonic unimolecular proton-transfer step results in a relatively small concentration of reaction products, thus slowing the rate of the following step such that it becomes rate limiting. Incomplete consideration of these points has led to discrepancies in interpretation of data from the literature. Our reanalysis of these data suggests that proton-transfer elementary reaction steps have a nonzero intrinsic free energy barrier, implying, in the parlance of Marcus theory, that there is non-negligible nuclear reorganization. Outcomes from our analyses are generalizable to inner-sphere electron-transfer reactions such as those involved in (photo)electrochemical fuel-forming reactions.

Quantification of Excited-State Brønsted-Lowry Acidity of Weak Photoacids Using Steady-State Photoluminescence Spectroscopy and a Driving-Force-Dependent Kinetic Theory

Photoacids and photobases constitute a class of molecules that upon absorption of light undergoes a reversible change in acidity, i.e. pK_a. Knowledge of the excited-state pK_a value, pK_a*, is critical for predicting excited-state proton-transfer behavior. A reasonable approximation of pK_a* is possible using the Förster cycle analysis, but only when the ground-state pK_a is known. This poses a challenge for the study of weak photoacids (photobases) with less acidic (basic) excited states (pK_a* (pK_b*) > 7), because ground-state pK_a (pK_b) values are >14, making it difficult to quantify them accurately in water. Another method to determine pK_a* relies on acid-base titrations with photoluminescence detection and Henderson-Hasselbalch analysis. This method requires that the acid dissociation reaction involving the thermally equilibrated electronic excited state reaches chemical quasi-equilibrium, which does not occur for weak photoacids (photobases) due to slow rates of excited-state proton transfer. Herein, we report a method to overcome these limitations. We demonstrate that liquid water and aqueous hydroxide are unique proton-accepting quenchers of excited-state photoacids. We determine that Stern-Volmer quenching analysis is appropriate to extract rate constants for excited-state proton transfer in aqueous solutions from a weak photoacid, 5-aminonaphthalene-1-sulfonate, to a series of proton-accepting quenchers. Analysis of these data by Marcus-Cohen bond-energy-bond-order theory yields an accurate value for pK_a* of 5-aminonaphthalene-1-sulfonate. Our method is broadly accessible because it only requires readily available steady-state photoluminescence spectroscopy. Moreover, our results for weak photoacids are consistent with those from previous studies of strong photoacids, each showing the applicability of kinetic theories to interpret driving-force-dependent rate constants for proton-transfer reactions.

Double Proton Transfer Across a Table: The Formic Acid Dimer-Fluorobenzene Complex

Proton transfer via tunneling is a fundamental quantum‐mechanical phenomenon. We report rotational spectroscopy measurements of this process in the complex of the formic acid dimer with fluorobenzene. The assignment of the spectrum indicates that this complex exists in the form of a π–π stacked structure. Each rotational transition of the parent isotopologue exhibits splitting. Isotopic substitution experiments show that the spectral splitting results from double‐proton transfer tunneling in the formic acid dimer. Presence of fluorobenzene as a neighboring molecule does not quench the double proton transfer in the formic acid dimer but decreases its tunneling splitting from 341(3) MHz to 267.608(1) MHz. Calculations suggest that the presence of the weakly bounded fluorobenzene does not influence the activation energy of the proton transfer. The fluorobenzene is reoriented with respect to the formic acid dimer during the course of the reaction, slowing down the proton transfer motion.

Electron Flow Characterization of Charge Transfer for Carbonic Acid to Strong Base Proton Transfer in Aqueous Solution

Protonation of the strong base methylamine CH₃NH₂ by carbonic acid H₂CO₃ in aqueous solution, HOCOOH···NH₂CH₃ → HOCOO^-···⁺HNH₂CH₃, has been previously studied ( J. Phys. Chem. B 2016, 109, 2271-2280; J. Phys. Chem. B 2016, 109, 2281-2290) via Car-Parinnello molecular dynamics. This proton transfer (PT) reaction within a hydrogen (H)-bonded complex was found to be barrierless and very rapid, with key reaction coordinates comprising the proton coordinate, the H-bond separation R_ON, and a solvent coordinate, reflecting the water solvent rearrangement involved in the neutral to ion pair conversion. In the present work, the reaction's charge flow aspects are analyzed in detail, especially a description via Mulliken charge transfer for PT (MCTPT). A natural bond orbital analysis and some extensions of them are employed for the complex's electronic structure during the reaction trajectories. Results demonstrate that consistent with the MCTPT picture, the charge transfer (CT) occurs from a methylamine base nonbonding orbital to a carbonic acid antibonding orbital. A complementary MCTPT reaction product perspective of CT from the antibonding orbital of the HN⁺ moiety to the nonbonding orbital of the oxygen in the H-bond complex is also presented. σ_OH and σ_HN⁺ bond order expressions show this CT to occur within the H-bond OHN triad, an aspect key for simultaneous bond-breaking and -forming in the PT reaction.

Low-Frequency Protein Motions Coupled to Catalytic Sites

This review examines low-frequency vibrational modes of proteins and their coupling to enzyme catalytic sites. That protein motions are critical to enzyme function is clear, but the kinds of motions present in proteins and how they are involved in function remain unclear. Several models of enzyme-catalyzed reaction suggest that protein dynamics may be involved in the chemical step of the catalyzed reaction, but the evidence in support of such models is indirect. Spectroscopic studies of low-frequency protein vibrations consistently show that there are underdamped modes of the protein with frequencies in the tens of wavenumbers where overdamped behavior would be expected. Recent studies even show that such underdamped vibrations modulate enzyme active sites. These observations suggest that increasingly sophisticated spectroscopic methods will be able to unravel the link between low-frequency protein vibrations and enzyme function.

Adduct under Field-A Qualitative Approach to Account for Solvent Effect on Hydrogen Bonding

The location of a mobile proton in acid-base complexes in aprotic solvents can be predicted using a simplified Adduct under Field (AuF) approach, where solute–solvent effects on the geometry of hydrogen bond are simulated using a fictitious external electric field. The parameters of the field have been estimated using experimental data on acid-base complexes in CDF₃/CDClF₂. With some limitations, they can be applied to the chemically similar CHCl₃ and CH₂Cl₂. The obtained data indicate that the solute–solvent effects are critically important regardless of the type of complexes. The temperature dependences of the strength and fluctuation rate of the field explain the behavior of experimentally measured parameters.

Ultrafast excited-state proton transfer dynamics in dihalogenated non-fluorescent and fluorescent GFP chromophores

Green fluorescent protein (GFP) has enabled a myriad of bioimaging advances due to its photophysical and photochemical properties. To deepen the mechanistic understanding of such light-induced processes, novel derivatives of GFP chromophore p-HBDI were engineered by fluorination or bromination of the phenolic moiety into superphotoacids, which efficiently undergo excited-state proton transfer (ESPT) in aqueous solution within the short lifetime of the excited state, as opposed to p-HBDI where efficient ESPT is not observed. In addition, we tuned the excited-state lifetime from picoseconds to nanoseconds by conformational locking of the p-HBDI backbone, essentially transforming the nonfluorescent chromophores into highly fluorescent ones. The unlocked superphotoacids undergo a barrierless ESPT without much solvent activity, whereas the locked counterparts exhibit two distinct solvent-involved ESPT pathways. Comparative analysis of femtosecond transient absorption spectra of these unlocked and locked superphotoacids reveals that the ESPT rates adopt an "inverted" kinetic behavior as the thermodynamic driving force increases upon locking the backbone. Further experimental and theoretical investigations are expected to shed more light on the interplay between the modified electronic structure (mainly by dihalogenation) and nuclear motions (by conformational locking) of the functionalized GFP derivatives (e.g., fluorescence on and off).

Intact carbonic acid is a viable protonating agent for biological bases

Carbonic acid H₂CO₃ (CA) is a key constituent of the universal CA/bicarbonate/CO₂ buffer maintaining the pH of both blood and the oceans. Here we demonstrate the ability of intact CA to quantitatively protonate bases with biologically-relevant pK_as and argue that CA has a previously unappreciated function as a major source of protons in blood plasma. We determine with high precision the temperature dependence of pK_a(CA), pK_a(T) = -373.604 + 16,500/T + 56.478 ln T. At physiological-like conditions pK_a(CA) = 3.45 (I = 0.15 M, 37 °C), making CA stronger than lactic acid. We further demonstrate experimentally that CA decomposition to H₂O and CO₂ does not impair its ability to act as an ordinary carboxylic acid and to efficiently protonate physiological-like bases. The consequences of this conclusion are far reaching for human physiology and marine biology. While CA is somewhat less reactive than (H⁺)_aq, it is more than 1 order of magnitude more abundant than (H⁺)_aq in the blood plasma and in the oceans. In particular, CA is about 70× more abundant than (H⁺)_aq in the blood plasma, where we argue that its overall protonation efficiency is 10 to 20× greater than that of (H⁺)_aq, often considered to be the major protonating agent there. CA should thus function as a major source for fast in vivo acid-base reactivity in the blood plasma, possibly penetrating intact into membranes and significantly helping to compensate for (H⁺)_aq's kinetic deficiency in sustaining the large proton fluxes that are vital for metabolic processes and rapid enzymatic reactions.

Nuclear Quantum Effects in Water Reorientation and Hydrogen-Bond Dynamics

We combine classical and ring polymer molecular dynamics simulations with the molecular jump model to provide a molecular description of the nuclear quantum effects (NQEs) on water reorientation and hydrogen-bond dynamics in liquid H₂O and D₂O. We show that while the net NQE is negligible in D₂O, it leads to a ∼13% acceleration in H₂O dynamics compared to a classical description. Large angular jumps-exchanging hydrogen-bond partners-are the dominant reorientation pathway (just as in a classical description); the faster reorientation dynamics arise from the increased jump rate constant. NQEs do not change the jump amplitude distribution, and no significant tunneling is found. The faster jump dynamics are quantitatively related to decreased structuring of the OO radial distribution function when NQEs are included. This is explained, via a jump model analysis, by competition between the effects of water's librational and OH stretch mode zero-point energies on the hydrogen-bond strength.

Reaction Mechanism for Direct Proton Transfer from Carbonic Acid to a Strong Base in Aqueous Solution II: Solvent Coordinate-Dependent Reaction Path

The protonation of methylamine base CH3NH2 by carbonic acid H2CO3 within a hydrogen (H)-bonded complex in aqueous solution was studied via Car-Parrinello dynamics in the preceding paper (Daschakraborty, S.; Kiefer, P. M.; Miller, Y.; Motro, Y.; Pines, D.; Pines, E.; Hynes, J. T. J. Phys. Chem. B 2016, DOI: 10.1021/acs.jpcb.5b12742). Here some important further details of the reaction path are presented, with specific emphasis on the water solvent's role. The overall reaction is barrierless and very rapid, on an ∼100 fs time scale, with the proton transfer (PT) event itself being very sudden (<10 fs). This transfer is preceded by the acid-base H-bond's compression, while the water solvent changes little until the actual PT occurrence; this results from the very strong driving force for the reaction, as indicated by the very favorable acid-protonated base ΔpKa difference. Further solvent rearrangement follows immediately the sudden PT's production of an incipient contact ion pair, stabilizing it by establishment of equilibrium solvation. The solvent water's short time scale ∼120 fs response to the incipient ion pair formation is primarily associated with librational modes and H-bond compression of water molecules around the carboxylate anion and the protonated base. This is consistent with this stabilization involving significant increase in H-bonding of hydration shell waters to the negatively charged carboxylate group oxygens' (especially the former H2CO3 donor oxygen) and the nitrogen of the positively charged protonated base's NH3(+).

Reaction Mechanism for Direct Proton Transfer from Carbonic Acid to a Strong Base in Aqueous Solution I: Acid and Base Coordinate and Charge Dynamics

Protonation by carbonic acid H2CO3 of the strong base methylamine CH3NH2 in a neutral contact pair in aqueous solution is followed via Car-Parrinello molecular dynamics simulations. Proton transfer (PT) occurs to form an aqueous solvent-stabilized contact ion pair within 100 fs, a fast time scale associated with the compression of the acid-base hydrogen-bond (H-bond), a key reaction coordinate. This rapid barrierless PT is consistent with the carbonic acid-protonated base pKa difference that considerably favors the PT, and supports the view of intact carbonic acid as potentially important proton donor in assorted biological and environmental contexts. The charge redistribution within the H-bonded complex during PT supports a Mulliken picture of charge transfer from the nitrogen base to carbonic acid without altering the transferring hydrogen's charge from approximately midway between that of a hydrogen atom and that of a proton.

How Acidic Is Carbonic Acid?

Carbonic, lactic, and pyruvic acids have been generated in aqueous solution by the transient protonation of their corresponding conjugate bases by a tailor-made photoacid, the 6-hydroxy-1-sulfonate pyrene sodium salt molecule. A particular goal is to establish the pK(a) of carbonic acid H2CO3. The on-contact proton transfer (PT) reaction rate from the optically excited photoacid to the carboxylic bases was derived, with unprecedented precision, from time-correlated single-photon-counting measurements of the fluorescence lifetime of the photoacid in the presence of the proton acceptors. The time-dependent diffusion-assisted PT rate was analyzed using the Szabo-Collins-Kimball equation with a radiation boundary condition. The on-contact PT rates were found to follow the acidity order of the carboxylic acids: the stronger was the acid, the slower was the PT reaction to its conjugate base. The pK(a) of carbonic acid was found to be 3.49 ± 0.05 using both the Marcus and Kiefer-Hynes free energy correlations. This establishes H2CO3 as being 0.37 pK(a) units stronger and about 1 pK(a) unit weaker, respectively, than the physiologically important lactic and pyruvic acids. The considerable acid strength of intact carbonic acid indicates that it is an important protonation agent under physiological conditions.

Solvent dependence of excited-state proton transfer from pyranine-derived photoacids

Steady-state and time-resolved techniques were employed to study the excited-state proton-transfer (ESPT) rate of two newly synthesized 8-hydroxy-1,3,6-pyrenetrisulfonate (pyranine, HPTS) derived photoacids in three protic solvents, water, methanol and ethanol. The ESPT rate constant k(PT) of tris(1,1,1,3,3,3-hexafluoropropan-2-yl)-8-hydroxypyrene-1,3,6-trisulfonate, 1a, whose pK(a)* ~ -4, in water, methanol and ethanol is 3 × 10(11) s(-1), 8 × 10(9) s(-1) and 5 × 10(9) s(-1) respectively. (8-Hydroxy-N1,N3,N6-tris(2-hydroxyethyl)-N1,N3,N6-trimethylpyrene-1,3,6 trisulfonamide, 1b) is a weaker acid than 1a but still a strong photoacid with pK(a)* ~ -1 and the ESPT rate in water, methanol and ethanol is 7 × 10(10) s(-1), 4 × 10(8) s(-1) and 2 × 10(8) s(-1). We qualitatively explain our kinetic results by a Marcus-like free-energy correlation which was found to have a general form suitable for describing proton transfer reactions in both the proton-adiabatic and the proton-non-adiabatic limits.

Fast photoinduced reactions in the condensed phase are nonexponential

Time-resolved measurements of photoinduced reactions reveal that many ultrafast reactions in the femto- to picosecond time scale are nonexponential. In this article we provide several examples of reactions that exhibit a nonexponential rate. We explain the wide range of the nonexponential reaction by the lack of time separation between τ(s), the characteristic fast equilibration time of the population in the reactant potential well, and the longer time τ(e), the characteristic time to cross the energy barrier between the reactant and the product.

Unveiling the Eigen-Weller ion pair from the excited state proton transfer kinetics of 3-chloro-4-methyl-7-hydroxycoumarin

The prototropic reactions of the first excited singlet state of 3-chloro-4-methylumbelliferone (3Cl4MU), in dioxane:water mixtures (Dx:H2O), were revisited using ps-time-resolved fluorescence techniques. The data response to the dielectric constant of the mixtures revealed the presence of an additional fourth kinetic species, kinetically coupled to the neutral (N*), the tautomeric (T*), and anionic (A(-)*) forms of 3Cl4MU, which is assigned to the elusive geminate (A(-)*···H(+)) ion pair. From the data analysis, all rate constants of the prototropic and diffusion processes involved were separately evaluated. The results showed that, whenever the geminate ionic pair is not kinetically detected, the evaluated values for deprotonation and protonation rate constants can substantially deviate from the real ones, depending on the efficiencies of pair recombination and dissociation. Finally, the results provide convincing kinetic evidence for the Eigen-Weller mechanism (intermediacy of the geminate ionic pair) in a quasi-aqueous medium, which to our knowledge had not yet been given.

Investigation of excited-state intramolecular proton transfer coupled charge transfer reaction of paeonol

An excited-state intramolecular proton transfer (ESIPT) coupled charge transfer reaction of paeonol was investigated both experimentally and theoretically. The ESIPT reaction of paeonol was predicted based on the large Stokes shift, which is observed in steady-state absorption and fluorescence spectra in an ethanol solution. The steady-state spectra in some solutions, such as methanol, ethanol, propanol, dichloromethane, and n-hexane, illustrate that the ESIPT reaction of paeonol has no dependence on the solvent properties. Therefore, the excited-state intermolecular proton transfer cannot be generated in protic solvents. Using the density functional theory and time-dependent density functional theory methods, we make a subsequent theoretical calculation that indicates that the ESIPT reaction of paeonol occurs through the intramolecular hydrogen bond O−H···O=C. The excited-state potential energy curve of paeonol indicates that the ESIPT reaction is a barrierless process, and the fluorescence emission of paeonol at 493 nm in the ethanol solution was assigned to the keto isomer fluorescence. Additionally, we also found an intramolecular charge transfer in the excited state by analysing the frontier molecular orbitals of paeonol.

Vibrational relaxation of chloroiodomethane in cold argon

Electronically exciting the C-I stretch in the molecule chloroiodomethane CH2ClI embedded in a matrix of argon at 12 K can lead to an isomer, iso-chloroiodomethane CH2Cl-I, that features a chlorine iodine bond. By temporally probing the isomer at two different frequencies of 435 nm and 485 nm, multiple timescales for isomerization and vibrational energy relaxation were inferred [T. J. Preston, et al., J. Chem. Phys. 135, 114503 (2011)]. This relaxation is studied theoretically using molecular dynamics by considering 2 and 3 dimensional models. Multiple decay rate constants of the same order of magnitude as the experiment are observed. These decay rate constants are interpreted within the context of the Landau-Teller theory. Sensitivity of the decay rate constants on the bath and system parameters shed more light into the mechanism of vibrational energy relaxation.

Functional significance of evolving protein sequence in dihydrofolate reductase from bacteria to humans

With the rapidly growing wealth of genomic data, experimental inquiries on the functional significance of important divergence sites in protein evolution are becoming more accessible. Here we trace the evolution of dihydrofolate reductase (DHFR) and identify multiple key divergence sites among 233 species between humans and bacteria. We connect these sites, experimentally and computationally, to changes in the enzyme's binding properties and catalytic efficiency. One of the identified evolutionarily important sites is the N23PP modification (∼mid-Devonian, 415-385 Mya), which alters the conformational states of the active site loop in Escherichia coli dihydrofolate reductase and negatively impacts catalysis. This enzyme activity was restored with the inclusion of an evolutionarily significant lid domain (G51PEKN in E. coli enzyme; ∼2.4 Gya). Guided by this evolutionary genomic analysis, we generated a human-like E. coli dihydrofolate reductase variant through three simple mutations despite only 26% sequence identity between native human and E. coli DHFRs. Molecular dynamics simulations indicate that the overall conformational motions of the protein within a common scaffold are retained throughout evolution, although subtle changes to the equilibrium conformational sampling altered the free energy barrier of the enzymatic reaction in some cases. The data presented here provide a glimpse into the evolutionary trajectory of functional DHFR through its protein sequence space that lead to the diverged binding and catalytic properties of the E. coli and human enzymes.

Accelerating slow excited state proton transfer

Visible light excitation of the ligand-bridged assembly [(bpy)(2)Ru(a)(II)(L)Ru(b)(II)(bpy)(OH(2))(4+)] (bpy is 2,2'-bipyridine; L is the bridging ligand, 4-phen-tpy) results in emission from the lowest energy, bridge-based metal-to-ligand charge transfer excited state (L(-•))Ru(b)(III)-OH(2) with an excited-state lifetime of 13 ± 1 ns. Near-diffusion-controlled quenching of the emission occurs with added HPO(4)(2-) and partial quenching by added acetate anion (OAc(-)) in buffered solutions with pH control. A Stern-Volmer analysis of quenching by OAc(-) gave a quenching rate constant of k(q) = 4.1 × 10(8) M(-1) • s(-1) and an estimated pK(a)* value of ~5 ± 1 for the [(bpy)(2)Ru(a)(II)(L(•-))Ru(b)(III)(bpy)(OH(2))(4+)]* excited state. Following proton loss and rapid excited-state decay to give [(bpy)(2)Ru(a)(II)(L)Ru(b)(II)(bpy)(OH)(3+)] in a H(2)PO(4)(-)/HPO(4)(2-) buffer, back proton transfer occurs from H(2)PO(4)(-) to give [(bpy)(2)Ru(a)(II)(L)Ru(b)(bpy)(OH(2))(4+)] with k(PT,2) = 4.4 × 10(8) M(-1) • s(-1). From the intercept of a plot of k(obs) vs. [H(2)PO(4)(-)], k = 2.1 × 10(6) s(-1) for reprotonation by water providing a dramatic illustration of kinetically limiting, slow proton transfer for acids and bases with pK(a) values intermediate between pK(a)(H(3)O(+)) = -1.74 and pK(a)(H(2)O) = 15.7.

Reaction pathways of proton transfer in hydrogen-bonded phenol-carboxylate complexes explored by combined UV-vis and NMR spectroscopy

Combined low-temperature NMR/UV-vis spectroscopy (UVNMR), where optical and NMR spectra are measured in the NMR spectrometer under the same conditions, has been set up and applied to the study of H-bonded anions A··H··X(-) (AH = 1-(13)C-2-chloro-4-nitrophenol, X(-) = 15 carboxylic acid anions, 5 phenolates, Cl(-), Br(-), I(-), and BF(4)(-)). In this series, H is shifted from A to X, modeling the proton-transfer pathway. The (1)H and (13)C chemical shifts and the H/D isotope effects on the latter provide information about averaged H-bond geometries. At the same time, red shifts of the π-π* UV-vis absorption bands are observed which correlate with the averaged H-bond geometries. However, on the UV-vis time scale, different tautomeric states and solvent configurations are in slow exchange. The combined data sets indicate that the proton transfer starts with a H-bond compression and a displacement of the proton toward the H-bond center, involving single-well configurations A-H···X(-). In the strong H-bond regime, coexisting tautomers A··H···X(-) and A(-)···H··X are observed by UV. Their geometries and statistical weights change continuously when the basicity of X(-) is increased. Finally, again a series of single-well structures of the type A(-)···H-X is observed. Interestingly, the UV-vis absorption bands are broadened inhomogeneously because of a distribution of H-bond geometries arising from different solvent configurations.

Proton transfer 200 years after von Grotthuss: insights from ab initio simulations

In the last decade, ab initio simulations and especially Car-Parrinello molecular dynamics have significantly contributed to the improvement of our understanding of both the physical and chemical properties of water, ice, and hydrogen-bonded systems in general. At the heart of this family of in silico techniques lies the crucial idea of computing the many-body interactions by solving the electronic structure problem "on the fly" as the simulation proceeds, which circumvents the need for pre-parameterized potential models. In particular, the field of proton transfer in hydrogen-bonded networks greatly benefits from these technical advances. Here, several systems of seemingly quite different nature and of increasing complexity, such as Grotthuss diffusion in water, excited-state proton-transfer in solution, phase transitions in ice, and protonated water networks in the membrane protein bacteriorhodopsin, are discussed in the realms of a unifying viewpoint.

Chance and design—Proton transfer in water, channels and bioenergetic proteins

Proton transfer and transport in water, gramicidin and some selected channels and bioenergetic proteins are reviewed. An attempt is made to draw some conclusions about how Nature designs long distance, proton transport functionality. The prevalence of water rather than amino acid hydrogen bonded chains is noted, and the possible benefits of waters as the major component are discussed qualitatively.

Nuclear-electronic orbital nonorthogonal configuration interaction approach

The nuclear-electronic orbital nonorthogonal configuration interaction (NEO-NOCI) approach is presented. In this framework, the hydrogen nuclei are treated quantum mechanically on the same level as the electrons, and a mixed nuclear-electronic time-independent Schrodinger equation is solved with molecular orbital techniques. For hydrogen transfer systems, the transferring hydrogen is represented by two basis function centers to allow delocalization of the nuclear wave function. In the two-state NEO-NOCI approach, the ground and excited state delocalized nuclear-electronic wave functions are expressed as linear combinations of two nonorthogonal localized nuclear-electronic wave functions obtained at the NEO-Hartree-Fock level. The advantages of the NEO-NOCI approach are the removal of the adiabatic separation between the electrons and the quantum nuclei, the computational efficiency, the potential for systematic improvement by enhancing the basis sets and number of configurations, and the applicability to a broad range of chemical systems. The tunneling splitting is determined by the energy difference between the two delocalized vibronic states. The hydrogen tunneling splittings calculated with the NEO-NOCI approach for the [He-H-He]+ model system with a range of fixed He-He distances are in excellent agreement with NEO-full CI and Fourier grid calculations. These benchmarking calculations indicate that NEO-NOCI is a promising approach for the calculation of delocalized, bilobal hydrogen wave functions and the corresponding hydrogen tunneling splittings.