Coupled-channels quantum theory of electronic flux density in electronically adiabatic processes: application to the hydrogen molecule ion

This article presents the results of the first quantum simulations of the electronic flux density (j(e)) by the "coupled-channels" (CC) theory, the fundamentals of which are presented in the previous article [Diestler, D. J. J. Phys. Chem. A 2012, DOI: 10.1021/jp207843z]. The principal advantage of the CC scheme is that it employs exclusively standard methods of quantum chemistry and quantum dynamics within the framework of the Born-Oppenheimer approximation (BOA). The CC theory goes beyond the BOA in that it yields a nonzero j(e) for electronically adiabatic processes, in contradistinction to the BOA itself, which always gives j(e) = 0. The CC is applied to oriented H(2)(+) vibrating in the electronic ground state ((2)Σ(g)(+)), for which the nuclear and electronic flux densities evolve on a common time scale of about 22 fs per vibrational period. The system is chosen as a touchstone for the CC theory, because it is the only one for which highly accurate flux densities have been calculated numerically without invoking the BOA [Barth et al, Chem. Phys. Lett. 2009, 481, 118]. Good agreement between CC and accurate results supports the CC approach, another advantage of which is that it allows a transparent interpretation of the temporal and spatial properties of j(e).     

Proton-coupled electron transfer in solution, proteins, and electrochemistry

Recent advances in the theoretical treatment of proton-coupled electron transfer (PCET) reactions are reviewed. These reactions play an important role in a wide range of biological processes, as well as in fuel cells, solar cells, chemical sensors, and electrochemical devices. A unified theoretical framework has been developed to describe both sequential and concerted PCET, as well as hydrogen atom transfer (HAT). A quantitative diagnostic has been proposed to differentiate between HAT and PCET in terms of the degree of electronic nonadiabaticity, where HAT corresponds to electronically adiabatic proton transfer and PCET corresponds to electronically nonadiabatic proton transfer. In both cases, the overall reaction is typically vibronically nonadiabatic. A series of rate constant expressions have been derived in various limits by describing the PCET reactions in terms of nonadiabatic transitions between electron-proton vibronic states. These expressions account for the solvent response to both electron and proton transfer and the effects of the proton donor-acceptor vibrational motion. The solvent and protein environment can be represented by a dielectric continuum or described with explicit molecular dynamics. These theoretical treatments have been applied to numerous PCET reactions in solution and proteins. Expressions for heterogeneous rate constants and current densities for electrochemical PCET have also been derived and applied to model systems.     

Calculation of vibronic couplings for phenoxyl/phenol and benzyl/toluene self-exchange reactions: implications for proton-coupled electron transfer mechanisms

The vibronic couplings for the phenoxyl/phenol and the benzyl/toluene self-exchange reactions are calculated with a semiclassical approach, in which all electrons and the transferring hydrogen nucleus are treated quantum mechanically. In this formulation, the vibronic coupling is the Hamiltonian matrix element between the reactant and product mixed electronic-proton vibrational wavefunctions. The magnitude of the vibronic coupling and its dependence on the proton donor-acceptor distance can significantly impact the rates and kinetic isotope effects, as well as the temperature dependences, of proton-coupled electron transfer reactions. Both of these self-exchange reactions are vibronically nonadiabatic with respect to a solvent environment at room temperature, but the proton tunneling is electronically nonadiabatic for the phenoxyl/phenol reaction and electronically adiabatic for the benzyl/toluene reaction. For the phenoxyl/phenol system, the electrons are unable to rearrange fast enough to follow the proton motion on the electronically adiabatic ground state, and the excited electronic state is involved in the reaction. For the benzyl/toluene system, the electrons can respond virtually instantaneously to the proton motion, and the proton moves on the electronically adiabatic ground state. For both systems, the vibronic coupling decreases exponentially with the proton donor-acceptor distance for the range of distances studied. When the transferring hydrogen is replaced with deuterium, the magnitude of the vibronic coupling decreases and the exponential decay with distance becomes faster. Previous studies designated the phenoxyl/phenol reaction as proton-coupled electron transfer and the benzyl/toluene reaction as hydrogen atom transfer. In addition to providing insights into the fundamental physical differences between these two types of reactions, the present analysis provides a new diagnostic for differentiating between the conventionally defined hydrogen atom transfer and proton-coupled electron transfer reactions.     

Power-law dependence of the melting temperature of ubiquitin on the volume fraction of macromolecular crowders

The dependence of the melting temperature increase (ΔT(m)) of the protein ubiquitin on the volume fraction (?) of several commonly used macromolecular crowding agents (dextran 6, 40, and 70 and ficoll 70) was quantitatively examined and compared to a recently developed theoretical crowding model, i.e., ΔT(m) ～ (R(g)∕R(c))(α)φ(α∕3). We found that in the current case this model correctly predicts the power-law dependence of ΔT(m) on φ but significantly overestimates the role of the size (i.e., R(c)) of the crowding agent. In addition, we found that for ubiquitin the exponent α is in the range of 4.1-6.5, suggesting that the relation of α=3∕(3ν-1) is a better choice for estimating α based on the Flory coefficient (ν) of the polypeptide chain. Taken together these findings highlight the importance of improving our knowledge and theoretical treatment of the microcompartmentalization of the commonly used model crowding agents.     

Proton-coupled electron transfer versus hydrogen atom transfer: generation of charge-localized diabatic states

The distinction between proton-coupled electron transfer (PCET) and hydrogen atom transfer (HAT) mechanisms is important for the characterization of many chemical and biological processes. PCET and HAT mechanisms can be differentiated in terms of electronically nonadiabatic and adiabatic proton transfer, respectively. In this paper, quantitative diagnostics to evaluate the degree of electron-proton nonadiabaticity are presented. Moreover, the connection between the degree of electron-proton nonadiabaticity and the physical characteristics distinguishing PCET from HAT, namely, the extent of electronic charge redistribution, is clarified. In addition, a rigorous diabatization scheme for transforming the adiabatic electronic states into charge-localized diabatic states for PCET reactions is presented. These diabatic states are constructed to ensure that the first-order nonadiabatic couplings with respect to the one-dimensional transferring hydrogen coordinate vanish exactly. Application of these approaches to the phenoxyl-phenol and benzyl-toluene systems characterizes the former as PCET and the latter as HAT. The diabatic states generated for the phenoxyl-phenol system possess physically meaningful, localized electronic charge distributions that are relatively invariant along the hydrogen coordinate. These diabatic electronic states can be combined with the associated proton vibrational states to generate the reactant and product electron-proton vibronic states that form the basis of nonadiabatic PCET theories. Furthermore, these vibronic states and the corresponding vibronic couplings may be used to calculate rate constants and kinetic isotope effects of PCET reactions.     

Resolution of racemic R.S-α-arylethylamine by a new resolving agent (R)thiazolidine-2-thione-4-carboxylic acid

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Structures and photoelectron spectroscopy of Cu(n)(BO2)m-(n, m=1, 2) clusters: observation of hyperhalogen behavior

The electronic structures of CuBO(2)(-), Cu(BO(2))(2)(-), Cu(2)(BO(2))(-), and Cu(2)(BO(2))(2)(-) clusters were investigated using photoelectron spectroscopy. The measured vertical and adiabatic detachment energies of these clusters revealed unusual properties of Cu(BO(2))(2) cluster. With an electron affinity of 5.07 eV which is larger than that of its BO(2) superhalogen (4.46 eV) building-block, Cu(BO(2))(2) can be classified as a hyperhalogen. Density functional theory based calculations were carried out to identify the ground state geometries and study the electronic structures of these clusters. Cu(BO(2)) and Cu(BO(2))(2) clusters were found to form chainlike structures in both neutral and anionic forms. Cu(2)(BO(2)) and Cu(2)(BO(2))(2) clusters, on the other hand, preferred a chainlike structure in the anionic form but a closed ringlike structure in the neutral form. Equally important, substantial differences between adiabatic detachment energies and electron affinities were found, demonstrating that correct interpretation of the experimental photoelectron spectroscopy data requires theoretical support not only in determining the ground state geometry of neutral and anionic clusters, but also in identifying their low lying isomers.     

On equilibrium structures of the water molecule

Equilibrium structures are fundamental entities in molecular sciences. They can be inferred from experimental data by complicated inverse procedures which often rely on several assumptions, including the Born-Oppenheimer approximation. Theory provides a direct route to equilibrium geometries. A recent high-quality ab initio semiglobal adiabatic potential-energy surface (PES) of the electronic ground state of water, reported by Polyansky et al. [ ibid. 299, 539 (2003)] and called CVRQD here, is analyzed in this respect. The equilibrium geometries resulting from this direct route are deemed to be of higher accuracy than those that can be determined by analyzing experimental data. Detailed investigation of the effect of the breakdown of the Born-Oppenheimer approximation suggests that the concept of an isotope-independent equilibrium structure holds to about 3 x 10(-5) A and 0.02 degrees for water. The mass-independent [Born-Oppenheimer (BO)] equilibrium bond length and bond angle on the ground electronic state PES of water is r(e) (BO)=0.957 82 A and theta e (BO)=104.48(5) degrees , respectively. The related mass-dependent (adiabatic) equilibrium bond length and bond angle of H2 (16)O is r(e) (ad)=0.957 85 A and theta e (ad)=104.50(0) degrees , respectively, while those of D2 (16)O are r(e) (ad)=0.957 83 A and theta e (ad)=104.49(0) degrees . Pure ab initio prediction of J=1 and 2 rotational levels on the vibrational ground state by the CVRQD PESs is accurate to better than 0.002 cm(-1) for all isotopologs of water considered. Elaborate adjustment of the CVRQD PESs to reproduce all observed rovibrational transitions to better than 0.05 cm(-1) (or the lower ones to better than 0.0035 cm(-1)) does not result in noticeable changes in the adiabatic equilibrium structure parameters. The expectation values of the ground vibrational state rotational constants of the water isotopologs, computed in the Eckart frame using the CVRQD PESs and atomic masses, deviate from the experimentally measured ones only marginally, especially for A0 and B0. The small residual deviations in the effective rotational constants are due to centrifugal distortion, electronic, and non-Born-Oppenheimer effects. The spectroscopic (nonadiabatic) equilibrium structural parameters of H2 16O, obtained from experimentally determined A'0 and B'0 rotational constants corrected empirically to obtain equilibrium rotational constants, are r(e) (sp)=0.957 77 A and theta e (sp)=104.48 degrees .     

Regioselective synthesis of quinazoline containing novel monoaryl ethers at room temperature

We are herein reporting the regioselective synthesis of quinazoline containing novel monoaryl ethers (quinazoline‐O‐Ar) ( 3a‐3j ) at room temperature without any catalyst. From commercially available 2,4‐dichloro‐6,7‐dimethoxyquinazoline ( 1 ), 4‐chloro was selectively substituted with variety of electronically rich, electronically poor and electronically neutral phenols ( 2a‐2j ). Reaction was carried out in DMF and NaH for 4‐6 hours at room temperature in fairly good yield. The products were purified (>98% pure, hplc) by crystallization to avoid the use of column chromatography.     

Numerical Convergence of the Sinc Discrete Variable Representation for Solving Molecular Vibrational States with a Conical Intersection in Adiabatic Representation

Within the Born-Oppenheimer (BO) approximation, nuclear motions of a molecule are often envisioned to occur on an adiabatic potential energy surface (PES). However, this single PES picture should be reconsidered if a conical intersection (CI) is present, although the energy is well below the CI. The presence of the CI results in two additional terms in the nuclear Hamiltonian in the adiabatic presentation, i.e., the diagonal BO correction (DBOC) and the geometric phase (GP), which are divergent at the CI. At the same time, there are cusps in the adiabatic PESs. Thus usually it is regarded that there is numerical difficulty in a quantum dynamics calculation for treating CI in the adiabatic representation. A popular numerical method in nuclear quantum dynamics calculations is the Sinc discrete variable representation (DVR) method. We examine the numerical accuracy of the Sinc DVR method for solving the Schr?dinger equation of a two dimensional model of two electronic states with a CI in both the adiabatic and diabatic representation. The results suggest that the Sinc DVR method is capable of giving reliable results in the adiabatic representation with usual density of the grid points, without special treatment of the divergence of the DBOC and the GP. The numerical uncertainty is not worse than that after the introduction of an arbitrary vector potential for accounting the GP, whose accurate form usually is not easy to obtain.     

Nuclear Coordinate dependence of electronic transition moments in orbitally forbidden transitions: A new interpretation of deuterium isotope effects

The nuclear coordinate dependence of electronic transtion moments has been investigated for the purpose of finding new interpretations of deuterium isotope effects on spectral intensities and radiative decay rates in orbitally forbidden electronic transitions. By using “AO following nuclei” wavefunctions as the building block for the electronic wavefunction in the adiabatic BO vibronic wavefunction, the spin-free hamiltonian is diagonalized to generate eigenfunctions and eigen-energies. It is found that the electronic transtion moments based on these eigenfunctions show dependences upon the vibrational modes which are not directly involved in vibronic coupling. This leads to interpretations of the deuterium isotope effects in T₁ → S₀ radiative transitions of aromatic hydrocarbons and S₀ → S₁ absorption in pyrazine which are not based on the conventional Herzberg—Teller or non-BO coupling.     

Proton exchange and protonation of substituted oxadiazoles in trifluoroacetic acid

The rates of NH? COOH proton exchange between 5-amino-( 1a ) and 5-N-methylamino-( 1b )3-[2-(5′-nitro-2′-furyl)vinyl]-1,2,4-oxadiazoles and trifluoroacetic acid (TFA) have been measured by NMR spectroscopy. The values of the first-order rate constant and thermodynamic parameters for 1a and 1b , respectively, are: k_app (sec^?1) = 820 and 40 (50°C), ΔF (kcal/mole) = 14·7 and 16·5, ΔH^# (kcal/mole) = 17·3 and 24·3 and ΔS^# (e.u.) = 17 and 34. The comparison of rate constants indicates that after correction for proton equivalency proton exchange in 1a is faster than in 1b by a factor of ten. The presence of an NH₂ proton resonance ( 1a ) and an N-methyl doublet (J = 5·0 Hz) between 0 and 30° ( 1b ) suggests that 1a and 1b are present as amines and not as imines in TFA.     

Accurate, two-state ab initio study of the ground and first-excited states of He2+, including exact treatment of all Born-Oppenheimer correction terms

Born-Oppenheimer (BO) potentials for the ground and first-excited electronic states of He2+ are determined using high level ab initio techniques for internuclear separations R of 1.2-100 bohrs and accurately fit to analytical functions. In the present formulation, the BO potentials are nuclear mass independent, and the corresponding BO approximation is obtained by ignoring four terms of the full rovibronic Hamiltonian. These four Born-Oppenheimer correction (BOC) terms are as follows: (1) mass polarization, (2) electronic orbital angular momentum, (3) first derivative with respect to R, and (4) second derivative with respect to R. In order to enable an exact rovibronic calculation, each of the four BOC terms are computed as a function of R, for the two electronic states and for their coupling, without any approximation or use of empirical parameters. Each of the BOC terms is found to make a contribution to the total energy over at least some portion of the range of R investigated. Interestingly, the most significant coupling contribution arises from the electronic orbital angular momentum term, which is evidently computed for the first time in this work. Although several BOC curves exhibit a nontrivial dependence on R, all are accurately fit to analytical functions. The resulting functions, together with the BO potentials, are used to compute exact rovibronic energy levels for 3He 3He+,3He 4He+) and 4He 4He+. Comparison to available high quality experimental data indicates that the present BOC potentials provide the most accurate representation currently available of both the low- and high-lying levels of the ground electronic state and the bound levels of the excited state.     

Syntheses and Characterizations of Luminescent Complexes [(BINAP)Pt(C≡CC_6H_4R-p)_2] (R = H, 1; CH_3, 2) (BINAP = 2,2’-Bis(diphenylphosphino)-1,1’-binaphthyl)

1 INTRODUCTION σ-Alkynyl complexes of platinum have attracted considerable attention over the last few years not only for their structural aspect and reactivity[1~5], but also for their role as building blocks for molecular materials with interesting properties[6~10]. These complexes are usually stabilized by neutral ligands, such as tertiary phosphines PR3, diphosphines, and so on. However, as far as we know, similar platinum acetylide compounds containing the chiral diphos- phine liga…     

Vibrational quenching of excitonic splittings in H-bonded molecular dimers: the electronic Davydov splittings cannot match experiment

The S(1)/S(2) state exciton splittings of symmetric doubly hydrogen-bonded gas-phase dimers provide spectroscopic benchmarks for the excited-state electronic couplings between UV chromophores. These have important implications for electronic energy transfer in multichromophoric systems ranging from photosynthetic light-harvesting antennae to photosynthetic reaction centers, conjugated polymers, molecular crystals, and nucleic acids. We provide laser spectroscopic data on the S(1)/S(2) excitonic splitting Δ(exp) of the doubly H-bonded o-cyanophenol (oCP) dimer and compare to the splittings of the dimers of (2-aminopyridine)(2), [(2AP)(2)], (2-pyridone)(2), [(2PY)(2)], (benzoic acid)(2), [(BZA)(2)], and (benzonitrile)(2), [(BN)(2)]. The experimental S(1)/S(2) excitonic splittings are Δ(exp) = 16.4 cm(-1) for (oCP)(2), 11.5 cm(-1) for (2AP)(2), 43.5 cm(-1) for (2PY)(2), and <1 cm(-1) for (BZA)(2). In contrast, the vertical S(1)/S(2) energy gaps Δ(calc) calculated by the approximate second-order coupled cluster (CC2) method for the same dimers are 10-40 times larger than the Δ(exp) values. The qualitative failure of this and other ab initio methods to reproduce the exciton splitting Δ(exp) arises from the Born-Oppenheimer (BO) approximation, which implicitly assumes the strong-coupling case and cannot be employed to evaluate excitonic splittings of systems that are in the weak-coupling limit. Given typical H-bond distances and oscillator strengths, the majority of H-bonded dimers lie in the weak-coupling limit. In this case, the monomer electronic-vibrational coupling upon electronic excitation must be accounted for; the excitonic splittings arise between the vibronic (and not the electronic) transitions. The discrepancy between the BO-based splittings Δ(calc) and the much smaller experimental Δ(exp) values is resolved by taking into account the quenching of the BO splitting by the intramolecular vibronic coupling in the monomer S(1) ← S(0) excitation. The vibrational quenching factors Γ for the five dimers (oCP)(2), (2AP)(2), (2AP)(2), (BN)(2), and (BZA)(2) lie in the range Γ = 0.03-0.2. The quenched excitonic splittings Γ[middle dot]Δ(calc) are found to be in very good agreement with the observed splittings Δ(exp). The vibrational quenching approach predicts reliable Δ(exp) values for the investigated dimers, confirms the importance of vibrational quenching of the electronic Davydov splittings, and provides a sound basis for predicting realistic exciton splittings in multichromophoric systems.     

Chain-length-dependent termination rate constant: Effect on molecular weight distributions formed by pulsed laser radical polymerization

For polymerization initiated by an arbitrary sequence of laser pulses a numerical technique for calculating molecular weight distributions (MWDs) is developed, which takes into consideration the chain length dependence of the termination rate constant k_t. The MWDs for methyl methacrylate and styrene are calculated by use of α and k₀ values (for the law k = k₀(i)^−α of termination of radicals with chain length i) and averages $ \overline {(i,{\rm }j)} $ (for rate constants k = k₀$ \overline {(i,{\rm }j)} $ of termination of radicals with different degrees of polymerization) taken from the literature. The dependences of the overall termination constant 〈k_t〉 on initiation parameters (pulse repetition rate (v) and pulse intensity for initiation by periodic laser pulses) are presented. Two methods are proposed for α and k₀ determination: (a) by experiments on polymerization with periodic laser pulses where monomer-to-polymer conversions per pulse are determined for different v; (b) by experiments on polymerization with packets of pulses where the constant k_p (the rate constant of propagation), α and k₀ can be determined simultaneously from MWD. For both methods simple analytical equations are derived for evaluation of the constants. The limits of application of the methods are determined by use of the numerical technique for MWD calculation.     

Accurate ab initio determination of the adiabatic potential energy function and the Born-Oppenheimer breakdown corrections for the electronic ground state of LiH isotopologues

High level ab initio potential energy functions have been constructed for LiH in order to predict vibrational levels up to dissociation. After careful tests of the parameters of the calculation, the final adiabatic potential energy function has been composed from: (a) an ab initio nonrelativistic potential obtained at the multireference configuration interaction with singles and doubles level including a size-extensivity correction and quintuple-sextuple ζ extrapolations of the basis, (b) a mass-velocity-Darwin relativistic correction, and (c) a diagonal Born-Oppenheimer (BO) correction. Finally, nonadiabatic effects have also been considered by including a nonadiabatic correction to the kinetic energy operator of the nuclei. This correction is calculated from nonadiabatic matrix elements between the ground and excited electronic states. The calculated vibrational levels have been compared with those obtained from the experimental data [J. A. Coxon and C. S. Dickinson, J. Chem. Phys. 134, 9378 (2004)]. It was found that the calculated BO potential results in vibrational levels which have root mean square (rms) deviations of about 6-7 cm(-1) for LiH and ～3 cm(-1) for LiD. With all the above mentioned corrections accounted for, the rms deviation falls down to ～1 cm(-1). These results represent a drastic improvement over previous theoretical predictions of vibrational levels for all isotopologues of LiH.     

Bond functions for AB initio calculations on polyatomic molecules hydrocarbons

Transferable gaussian CH and CC bond functions and a C lone-pair function were optimized and compared to conventional polarization functions. The exponents (α) and position (γ,β) of these functions are α = 0.9, γ = 0.27 for CH bonds; α = 1.2, γ = 0.50 for CC bonds; α = 0.3, β = 0.47 for C lone-pair.     

Energetics of direct and water-mediated proton-coupled electron transfer

Proton-coupled electron transfer (PCET) is an elementary chemical reaction crucial for biological oxidoreduction. We perform quantum chemical calculations to study the direct and water-mediated PCET between two stacked tyrosines, TyrO(?) + TyrOH → TyrOH + TyrO(?), to mimic a key step in the catalytic reaction of class Ia ribonucleotide reductase (RNR). The energy surfaces of electronic ground and excited states are separated by a large gap of ~20 kcal mol(-1), indicative of an electronically adiabatic transfer mechanism. In response to chemical substitutions of the proton donor, the energy of the transition state for direct PCET shifts by exactly half of the change in energetic driving force, resulting in a linear free energy relation with a Br?nsted slope of ?. In contrast, for water-mediated PCET, we observe integer Br?nsted slopes of 1 and 0 for proton acceptor and donor modifications, respectively. Our calculations suggest that the π-stacking of the tyrosine dimer in RNR results in strong electronic coupling and adiabatic PCET. Water participation in the PCET can be identified perturbatively in a Br?nsted analysis.     

Syntheses and Characterizations of Luminescent Complexes [(BINAP)Pt(C≡CC6H4R-p)2] (R = H, 1; CH3, 2) (BINAP = 2,2''-Bis(diphenylphosphino)-1,1''-binaphthyl)

[(BINAP)Pt(C≡CC6H4R-p)2] (R = H, 1; CH3, 2) (BINAP = 2,2'-bis(diphenylphos- phino)-1,1'-binaphthyl) were synthesized and characterized by X-ray crystallography. Complex 1 crystallizes in triclinic, space group P with a = 11.699(3), b = 12.512(3), c = 15.611(4)(A), α = 93.277(3),β= 97.626(2), γ = 97.375(14)o, V = 2239.9(9)(A)3, Mr = 1014.92, Z = 2, Dc = 1.505 g/cm3, F(000) = 1010, μ(MoKα) = 3.244 mm-1, the final R = 0.0338 and wR = 0.0905 for 7738 observed reflections (I > 2σ(I)). Complex 2 crystallizes in monoclinic, space group P21/n with a = 18.03690 (10), b = 13.06060(10), c = 21.6913(3)(A), β= 96.5430(10)o, V = 5076.60(9)(A)3, Mr = 1132.94, Z = 4, Dc = 1.482 g/cm3, F(000) = 2272, μ(MoKα) = 2.973 mm-1, the final R = 0.0481 and wR = 0.0893 for 8916 observed reflections (I > 2σ(I)). Both complexes emit intensively photoluminescence in both solid state and fluid solution due to MLCT (Pt→-C≡CC6H4R-p) emissive state.