Quantum Stabilization of the Frustrated Hydrogen Bonding Structure in the Hydrogen Fluoride Trimer.

We performed ab initio path integral molecular dynamics (PIMD) and molecular dynamics (MD) simulations to discuss the thermal and nuclear quantum effects on the stabilities of hydrogen bonding network in a hydrogen fluoride trimer (HF)3 cluster. By the conventional molecular orbital calculation, the (HF)3 cluster has an equilateral triangle shape, which has a frustration in the chemical structure of the hydrogen bonds, whereas the hydrogen bonding structure of a hydrogen fluoride dimer (HF)2 cluster is nearly perpendicular to the acceptor molecule. The ratio of the triangular structures with the three hydrogen bondings in the PIMD simulation is larger than that in the MD one, whereas nonhydrogen bonding conformations such as a dimerlike structure are often found in MD simulation. The nuclear quantum effect stabilizes the frustrated hydrogen bonding network of the triangular (HF)3 cluster.

Quantum fluctuations of a fullerene cage modulate its internal magnetic environment.

To investigate the effect of quantum fluctuations on the magnetic environment inside a C60 fullerene cage, we have calculated the nuclear magnetic shielding constant of protons in H2@C60 and HD@C60 systems by on-the-fly ab initio path integral simulation, including both thermal and nuclear quantum effects. The most dominant upfield from an isolated hydrogen molecule occurs due to the diamagnetic current of the C60 cage, which is partly cancelled by the paramagnetic current, where the paramagnetic contribution is enlarged by the zero-point vibrational fluctuation of the C60 carbon backbone structure via a widely distributed HOMO-LUMO gap. This quantum modulation mechanism of the nuclear magnetic shielding constant is newly proposed. Because this quantum effect is independent of the difference between H2 and HD, the H2/HD isotope shift occurs in spite of the C60 cage. The nuclear magnetic constants computed for H2@C60 and HD@C60 are 32.047 and 32.081 ppm, respectively, which are in reasonable agreement with the corresponding values of 32.19 and 32.23 ppm estimated from the experimental values of the chemical shifts.

Aminooxy-naphthylpropionic acid and its derivatives are inhibitors of auxin biosynthesis targeting l-tryptophan aminotransferase: structure-activity relationships.

We previously reported l-α-aminooxy-phenylpropionic acid (AOPP) to be an inhibitor of auxin biosynthesis, but its precise molecular target was not identified. In this study we found that AOPP targets TRYPTOPHAN AMINOTRANSFERASE of ARABIDOPSIS 1 (TAA1). We then synthesized 14 novel compounds derived from AOPP to study the structure-activity relationships of TAA1 inhibitors in vitro. The aminooxy and carboxy groups of the compounds were essential for inhibition of TAA1 in vitro. Docking simulation analysis revealed that the inhibitory activity of the compounds was correlated with their binding energy with TAA1. These active compounds reduced the endogenous indole-3-acetic acid (IAA) content upon application to Arabidopsis seedlings. Among the compounds, we selected 2-(aminooxy)-3-(naphthalen-2-yl)propanoic acid (KOK1169/AONP) and analyzed its activities in vitro and in vivo. Arabidopsis seedlings treated with KOK1169 showed typical auxin-deficient phenotypes, which were reversed by exogenous IAA. In vitro and in vivo experiments indicated that KOK1169 is more specific for TAA1 than other enzymes, such as phenylalanine ammonia-lyase. We further tested 41 novel compounds with aminooxy and carboxy groups to which we added protection groups to increase their calculated hydrophobicity. Most of these compounds decreased the endogenous auxin level to a greater degree than the original compounds, and resulted in a maximum reduction of about 90% in the endogenous IAA level in Arabidopsis seedlings. We conclude that the newly developed compounds constitute a class of inhibitors of TAA1. We designated them 'pyruvamine'.

Solvent Dependence of Double Proton Transfer in the Formic Acid-Formamidine Complex: Path Integral Molecular Dynamics Investigation.

Solvent dependence of double proton transfer in the formic acid-formamidine (FA-FN) complex at room temperature was investigated by means of ab initio path integral molecular dynamics (AIPIMD) simulation with taking nuclear quantum and thermal effects into account. The conductor-like screening model (COSMO) was applied for solvent effect. In comparison with gas phase, double proton delocalization between two heavy atoms (O and N) in FA-FN were observed with reduced proton transfer barrier height in low dielectric constant medium (<4.8). For dielectric constant medium at 4.8, the chance of finding these two protons are more pronounced due to the solvent effect which completely washes out the proton transfer barrier. In the case of higher dielectric constant medium (>4.8), the ionic species becomes more stable than the neutral ones and the formate anion and formamidium cation are thermodynamically stable. For ab initio molecular dynamics simulation, in low dielectric constant medium (<4.8) a reduction of proton transfer barrier with solvent effect is found to be less pronounced than the AIPIMD due to the absence of nuclear quantum effect. Moreover, the motions of FA-FN complex are significantly different with increasing dielectric constant medium. Such a difference is revealed in detail by the principal component analysis.

Efficient algorithms for semiclassical instanton calculations based on discretized path integrals.

Path integral instanton method is a promising way to calculate the tunneling splitting of energies for degenerated two state systems. In order to calculate the tunneling splitting, we need to take the zero temperature limit, or the limit of infinite imaginary time duration. In the method developed by Richardson and Althorpe [J. Chem. Phys. 134, 054109 (2011)], the limit is simply replaced by the sufficiently long imaginary time. In the present study, we have developed a new formula of the tunneling splitting based on the discretized path integrals to take the limit analytically. We have applied our new formula to model systems, and found that this approach can significantly reduce the computational cost and gain the numerical accuracy. We then developed the method combined with the electronic structure calculations to obtain the accurate interatomic potential on the fly. We present an application of our ab initio instanton method to the ammonia umbrella flip motion.

Review: Pathway analysis for peptide-mediated electronic coupling in the super-exchange mechanism of ET and EET.

Electron and excitation energy transfers (ET and EET) have an important role in biological energy-exchange processes. Proteins are an inhomogeneous and anisotropic medium for ET and EET. The protein structure influences electronic coupling, an important factor for ET and EET. The structure factor may be predicted by obtaining information about the tunneling pathways. The present paper mainly focuses on tunneling pathway analysis using the tunneling current (flux) of the electron or configuration density. The tunneling pathways for ET and singlet EET through peptides are introduced using tunneling current (flux) analysis. These tunneling pathways differ greatly between ET and singlet EET. This paper also reviews both the theoretical background and other methods for determining electronic tunneling pathways. These pathways are related to the effect of protein coordinates on the electronic coupling between the initial and final states of the ET and EET.

Bridge-mediated excitation energy transfer pathways through protein media: a Slater determinant-based electronic coupling calculation combined with localized molecular orbitals.

A computational method for calculating electronic coupling and pathway of electron transfer (ET) has been extended to that for excitation energy transfer (EET). A molecular orbital (MO)-based description has been generalized to one based on Slater determinants. This approach reduces the approximations used for the Green's function method from the perturbation of chemical-bond interactions to the perturbation of the configuration interactions. It is, therefore, reasonable to apply this method to EET, which involves the transfer of an electron-hole pair. To represent EET donor, acceptor, and bridge states, we adopted recently developed localized molecular orbitals (LMOs) for constructing locally excited determinants. The LMO approach provides a chemically meaningful interpretation of how each local excitation on the bridge contributes to the total electronic coupling of the EET. We applied the method to six model peptides and calculated their electronic couplings as well as the direct and through-peptide terms. Although the through-peptide term is usually negligibly small compared with the direct term, it can dominate the EET reaction in appropriate situations. The direct term dominates in long-range interactions because the indirect term decays in shorter distances.

First-principles calculations of the epsilon phase of solid oxygen.

The crystal, electronic and magnetic structures of solid oxygen in the epsilon phase have been investigated using the strongly constrained appropriately normed (SCAN) + rVV10 method and the generalized gradient approximation (GGA) + vdW-D + U method. The spin-polarized SCAN + rVV10 method with an 8-atom primitive unit cell provides lattice parameters consistent with the experimental results over the entire pressure range, including the epsilon-zeta structural phase transition at high pressure, but does not provide accurate values of the intermolecular distances d1 and d2 at low pressure. The agreement between the intermolecular distances and the experimental values is greatly improved when a 16-atom conventional unit cell is used. Therefore, the SCAN + rVV10 method with a 16-atom unit cell can be considered the most suitable model for the epsilon phase of solid oxygen. The spin-polarized SCAN + rVV10 model predicts a magnetic phase at low pressure. Since the lattice parameters of the predicted magnetic structure are consistent with the experimental lattice parameters measured at room temperature, our results may suggest that the epsilon phase is magnetic even at room temperature. The GGA + vdW-D + U (with an ad hoc value of Ueff = 2 eV at low pressure instead of the first-principles value of Ulreff ~ 9 eV) and hybrid functional methods provide similar results to the SCAN + rVV10 method; however, they do not provide reasonable values for the intermolecular distances.

Conformationally averaged score functions for electronic propagation in proteins.

We explore the influence of conformational dynamics on protein-mediated electron donor-acceptor interactions. We introduce a thermally averaged score function to characterize electronic propagation from redox cofactors into the protein and solvent. The score function is explored for myoglobin at the extended-Hückel level, and the results are compared with those of simpler models. The conformationally averaged quantum results are consistent with the empirical analysis of the Pathways model. Notably, subtle effects of quantum interference among multiple coupling pathways that arise in static structures are largely averaged out when protein thermal motion is included. Propagation through bulk water near the single-protein interface decays rapidly with distance.

Interference, fluctuation, and alternation of electron tunneling in protein media. 1. Two tunneling routes in photosynthetic reaction center alternate due to thermal fluctuation of protein conformation.

Electron tunneling routes for the electron transfer from the bacteriopheophytin anion to the primary quinone in the bacterial photosynthetic reaction center of Rhodobactor sphaeroides are investigated by a combined method of molecular dynamics simulations for the protein conformation fluctuation and quantum chemical calculations for the electronic states of the donor, acceptor, and protein medium. The analysis of the tunneling route is made by mapping interatomic electron tunneling currents for each protein conformation. We found that there are two dominant routes mainly passing through Trp(M252) (Trp route) or mainly passing through Met(M218) (Met route). Actual electron tunneling pathways alternate between the two routes, depending on the protein conformation which varies with time. When either the Trp route or the Met route dominates, the electron tunneling matrix element /T(DA)/ becomes large. When both the Trp route and the Met route dominate, /T(DA)/ becomes very small due to the destructive interference of the electron tunneling currents between the two routes. We found that a linear relationship exists between the value of /T(DA)/ and the inverse of the degree of destructive interference Q for a wide range of values (ca. 3-10(3) for Q). A similar relationship was also found previously for electron transfer in ruthenium-modified azurins, suggesting that this relationship holds true in general. From these results, we are led to the conclusion that /T(DA)/ cannot exceed a maximum value at Q = 1, even if much variation of /T(DA)/ happens due to the fluctuation of protein conformation. We also conclude that the property of the electron transfer alternates between constructive and destructive interference, due to the fluctuation of protein conformation. It is impossible to keep a system in either constructive or destructive interference because thermal fluctuation of protein conformation takes place.

Interference, fluctuation, and alternation of electron tunneling in protein media. 2. Non-condon theory for the energy gap dependence of electron transfer rate.

Developing the quantum transition rate theory of Prezhdo and Rossky (J. Chem. Phys. 1997, 107, 5863), we produced a new non-Condon theory of the rate of electron transfer (ET) which happens through a protein medium with conformational fluctuation. The new theory is expressed by a convolution form of the power spectrum for the autocorrelation function of the electronic tunneling matrix element T(DA)(t) with quantum correction and the ordinary Franck-Condon factor. The new theory satisfies the detailed balance condition for the forward and backward ET rates. The ET rate formula is divided into two terms of elastic and inelastic tunneling mechanisms on the mathematical basis. The present theory is applied to the ET from Bph(-) to Q(A) in the reaction center of Rhodobacter sphaeroides. Numerical calculations of T(DA)(t) were made by a combined method of molecular dynamics simulations and quantum chemistry calculations. We showed that the normalized autocorrelation function of T(DA)(t) is almost expressed by exponential forms. The calculated energy gap law of the ET rate is nearly Marcus' parabola in most of the normal region and around the maximum region, but it does not decay substantially in the inverted region, which is called the anomalous inverted region. We also showed that the energy gap law at the high uphill energy gap in the normal region is elevated considerably from the Marcus' parabola, which is called the anomalous normal region. Those anomalous energy gap laws are due to the inelastic tunneling mechanism which works actively at the energy gap far from zero. We presented an empirical formula for easily calculating the non-Condon ET rate, which is usable by many researchers. We provided experimental evidence for the anomalous inverted region which was basically reproduced by the present theory. The present theory was extensively compared with the previous non-Condon theories.

A Configuration Interaction Picture for a Molecular Environment Using Localized Molecular Orbitals: The Excited States of Retinal Proteins.

Electronic excitations of chromophores in proteins and solutions are associated with the electronic response of the molecular environment. The underlying interactions are important origins of solvatochromism. We performed large-scale configuration interaction singles (CIS) calculations (up to 1000 atoms) for retinal chromophores in proteins and methanol solution, in which one-electron processes (polarization and charge-transfer effects of the environment) are included. The present approach also improved the electrostatic potential, as compared to that described by a molecular mechanics (MM) force field. The CIS results were combined with the symmetry adapted cluster (SAC)-CI result using our own N-layer integrated molecular orbital molecular mechanics (ONIOM) method. As compared to the MM description, the CIS reduces the calculated excitation energy by 0.1-0.3 eV and also improves the relative excitation energies among retinal proteins. We applied our localized molecular orbital (LMO) transformation scheme to analyze the CI wave functions. The result clarified the contributions of the amino acids. In bacteriorhodopsin, Tyr185 contributes intermolecular CT excitations. The radial distribution of amino acids' contributions to the CI wave function was also analyzed. The results of the analysis are useful not only for understanding the molecular interactions and the role of amino acids in color tuning, but also for providing insight into the structure of the excited-state wave function for the molecular environment. An excitation-energy decomposition analysis also supported the results of the excited-state wave functions.

Protein Free Energy Corrections in ONIOM QM:MM Modeling: A Case Study for Isopenicillin N Synthase (IPNS).

The protein environment can have significant effects on the enzyme catalysis even though the reaction occurs locally at the reaction center. In this paper, we describe an efficient scheme that includes a classical molecular dynamics (MD) free-energy perturbation (FEP) correction to the reaction energy diagram, as a complement to the protein effect obtained from static ONIOM (QM:MM) calculations. The method is applied to eight different reaction steps, from the O2-bound reactant to formation of a high-valent ferryl-oxo intermediate, in the nonheme iron enzyme isopenicillin N synthase (IPNS), for which the QM:MM energy diagram has previously been computed [ Lundberg , M. et al. J. Chem. Theory Comput. 2009 , 5 , 220 - 234 ]. This large span of the reaction coordinate is covered by dividing each reaction step into microsteps using a virtual reaction coordinate, thus only requiring ONIOM information about the stationary points themselves. Protein effects are important for C-H bond activation and heterolytic O-O bond cleavage because both these two steps involve charge transfer, and compared to a static QM:MM energies, the dynamics of the protein environment changes the barrier for O-O bond cleavage by several kcal/mol. The origin of the dynamical contribution is analyzed in two terms, the geometrical effect caused by the change in average protein geometry (compared to the optimized geometry) in the room temperature MD simulation with the solvent, and the statistical (entropic) effect resulting from fluctuations in the interactions between the active site and the protein environment. These two effects give significant contributions in different steps of the reaction.

Transition States in a Protein Environment - ONIOM QM:MM Modeling of Isopenicillin N Synthesis.

To highlight the role of the protein in metal enzyme catalysis, we optimize ONIOM QM:MM transition states and intermediates for the full reaction of the nonheme iron enzyme isopenicillin N synthase (IPNS). Optimizations of transition states in large protein systems are possible using our new geometry optimizer with quadratic coupling between the QM and MM regions [Vreven, T. et al. Mol. Phys. 2006, 104, 701-704]. To highlight the effect of the metal center, results from the protein model are compared to results from an active site model containing only the metal center and coordinating residues [Lundberg, M. et al. Biochemistry 2008, 47, 1031-1042]. The analysis suggests that the main catalytic effect comes from the metal center, while the protein controls the reactivity to achieve high product specificity. As an example, hydrophobic residues align the valine substrate radical in a favorable conformation for thiazolidine ring closure and contribute to product selectivity and high stereospecificity. A low-barrier pathway for ß-lactam formation is found where the proton required for heterolytic O-O bond cleavage comes directly from the valine N-H group of the substrate. The alternative mechanism, where the proton in O-O bond cleavage initially comes from an iron water ligand, can be disfavored by the electrostatic interactions with the surrounding protein. Explicit protein effects on transition states are typically 1-6 kcal/mol in the present enzyme and can be understood by considering whether the transition state involves large movements of the substrate as well as whether it involves electron transfer.

Protein dynamics and electron transfer: electronic decoherence and non-Condon effects.

We compute the autocorrelation function of the donor-acceptor tunneling matrix element for six Ru-azurin derivatives. Comparison of this decay time to the decay time of the time-dependent Franck-Condon factor {computed by Rossky and coworkers [Lockwood, D. M., Cheng, Y.-K. & Rossky, P. J. (2001) Chem. Phys. Lett. 345, 159-165]} reveals the extent to which non-Condon effects influence the electron-transfer rate. is studied as a function of donor-acceptor distance, tunneling pathway structure, tunneling energy, and temperature to explore the structural and dynamical origins of non-Condon effects. For azurin, the correlation function is remarkably insensitive to tunneling pathway structure. The decay time is only slightly shorter than it is for solvent-mediated electron transfer in small organic molecules and originates, largely, from fluctuations of valence angles rather than bond lengths.