A New ab-Initio Approach for NMR Chemical Shifts in Periodic Systems

First-Principles Calculations within Periodic Boundary Conditions of the NMR Shielding Tensor for a Transition Metal Nucleus in a Solid State System: The Example of 51V in AlVO4

We present the first density functional theory based calculations of NMR shielding parameters for a transition metal nucleus using periodic boundary conditions. These calculations employ the gauge-including projected augmented-wave pseudopotential approach. The quality of this method is discussed by comparing experimental and calculated chemical shift tensor eigenvalues for the quadrupolar 51V nucleus in the diamagnetic solid-state compound AlVO4. Furthermore, the combination of shielding tensor with fast and accurate projector augmented-wave electric field gradient tensor calculations allows us to determine the relative orientation of these two tensors.

Proton transfer in imidazole-based molecular crystals

Heterocycles' aggregates show rather good proton conductivity. In particular, condensed structures formed by imidazole rings that are held together by polymeric chains have attracted some interest as possible candidate materials for fuel cell membranes. However, the details of the proton diffusion process could not be resolved by means of experimental measurements because of the fast rearrangement of the structure after each proton exchange. In this work, we report in detail the results of ab initio molecular dynamics calculations, which were briefly presented in a previous Letter [M. Iannuzzi and M. Parrinello, Phys. Rev. Lett. 93, 025901 (2004)]. The conformational changes associated with the diffusion of protons in model crystalline structures containing chains of imidazole rings are described in the framework of an atomistic approach. In particular, the bonding pattern characterizing the structure of imidazole-2-ethylene-oxide doped by an excess proton is also studied through the calculation of the 1H NMR chemical shifts. The unresolved resonances appearing in the experimental spectra could be associated with specific structural features, in connection with the fluctuating hydrogen bonding. The analysis of the distortions that induce or are induced by the mobility of the protons offers some new hints for the engineering of new proton conducting materials.

Interplay of Stereoelectronic and Enviromental Effects in Tuning the Structural and Magnetic Properties of a Prototypical Spin Probe: Further Insights from a First Principle Dynamical Approach

The nitrogen isotropic hyperfine coupling constant (hcc) and the g tensor of a prototypical spin probe (di-tert-butyl nitroxide, DTBN) in aqueous solution have been investigated by means of an integrated computational approach including Car-Parrinello molecular dynamics and quantum mechanical calculations involving a discrete-continuum embedding. The quantitative agreement between computed and experimental parameters fully validates our integrated approach. Decoupling of the structural, dynamical, and environmental contributions acting onto the spectral observables allows an unbiased judgment of the role played by different effects in determining the overall experimental observables and highlights the importance of finite-temperature vibrational averaging. Together with their intrinsic interest, our results pave the route toward more reliable interpretations of EPR parameters of complex systems of biological and technological relevance.

Solid-state NMR and computational studies of 4-methyl-2-nitroacetanilide

Studies on the solid-state structure of two polymorphs of 4-methyl-2-nitroacetanilide (MNA) were conducted using magic-angle spinning (13)C, (15)N and (1)H NMR spectroscopy, together with first-principles computations of NMR shielding (including use of a program that takes explicit account of the translational symmetry inherent in crystalline structures). The effects on (13)C chemical shifts of side-chain rotations have been explored. Information derived from these studies was then incorporated within a systematic space-search methodology for elucidation of trial crystallographic structures from powder XRD.

Spectroscopic Properties in the Liquid Phase: Combining High-Level Ab Initio Calculations and Classical Molecular Dynamics

We present an integrated computational tool, rooted in density functional theory, the polarizable continuum model, and classical molecular dynamics employing spherical boundary conditions, to study the spectroscopic observables of molecules in solution. As a test case, a modified OPLS-AA force field has been developed and used to compute the UV and NMR spectra of acetone in aqueous solution. The results show that provided the classical force fields are carefully reparameterized and validated, the proposed approach is robust and effective, and can also be used by nonspecialists to provide a general and powerful complement to experimental techniques.

Current Densities and Nucleus-Independent Chemical Shift Maps from Reciprocal-Space Density Functional Perturbation Theory Calculations

A method to calculate condensed-matter nucleus independent chemical shift maps (NICS maps) from first principles in the framework of density functional theory is presented. I use a pseudopotential plane-wave approach in which the electronic current density and the NICS map are obtained from an inverse Fourier transformation of the induced magnetic field represented in reciprocal space (G space). Due to its intrinsically periodic description, the method is suitable for isolated molecules (by using a supercell technique) and for condensed-phase systems like solids. The periodic NICS method was applied to hydrogen-bonded calixhydroquinone nanotubes, crystalline graphite, and two carbon nanotube systems.

Simulation of59Co NMR Chemical Shifts in Aqueous Solution

59Co chemical shifts were computed at the GIAO-B3LYP level for [Co(CN)6]3-, [Co(H2O)6]3+, [Co(NH3)6]3+, and [Co(CO)4]- in water. The aqueous solutions were modeled by Car-Parrinello molecular dynamics (CPMD) simulations, or by propagation on a hybrid quantum-mechanical/molecular-mechanical Born-Oppenheimer surface (QM/MM-BOMD). Mean absolute deviations from experiment obtained with these methods are on the order of 400 and 600 ppm, respectively, over a total delta(59Co) range of about 18,000 ppm. The effect of the solvent on delta(59Co) is mostly indirect, resulting primarily from substantial metal-ligand bond contractions on going from the gas phase to the bulk. The simulated solvent effects on geometries and delta(59Co) values are well reproduced by using a polarizable continuum model (PCM), based on optimization and perturbational evaluation of quantum-mechanical zero-point corrections.

Binding of Phosphinate and Phosphonate Inhibitors to Aspartic Proteases: A First-Principles Study

Phosphinate and phosphonate derivatives are potent inhibitors of aspartic proteases (APs). The affinity for the enzyme might be caused by the presence of low barrier hydrogen bonds between the ligand and the catalytic Asp dyad in the cleavage site. We have used density functional theory calculations along with hybrid quantum mechanics/molecular mechanics Car-Parrinello molecular dynamics simulations to investigate the hydrogen-bonding pattern at the binding site of the complexes of human immunodeficiency virus type-1 AP and the eukaryotic endothiapepsin and penicillopepsin. Our calculations are in fair agreement with the NMR data available for endothiapepsin (Coates et al. J. Mol. Biol. 2002, 318, 1405-1415) and show that the most stable active site configuration is the diprotonated, negatively charged form. In the viral complex both protons are located at the catalytic Asp dyad, while in the eukaryotic complexes the proton shared by the closest oxygen atoms is located at the phosphinic/phosphonic group.

Fraction of boroxol rings in vitreous boron oxide from a first-principles analysis of Raman and NMR spectra

We determine the fraction f of B atoms belonging to boroxol rings in vitreous boron oxide through a first-principles analysis. After generating a model structure of vitreous B2O3 by first-principles molecular dynamics, we address a large set of properties, including the neutron structure factor, the neutron density of vibrational states, the infrared spectra, the Raman spectra, and the 11B NMR spectra, and find overall good agreement with corresponding experimental data. From the analysis of Raman and 11B NMR spectra, we yield consistently for both probes a fraction f of approximately 0.75. This result indicates that the structure of vitreous boron oxide is largely dominated by boroxol rings.

Orbital magnetization in periodic insulators

Working in the Wannier representation, we derive an expression for the orbital magnetization of a periodic insulator. The magnetization is shown to be comprised of two contributions, an obvious one associated with the internal circulation of bulklike Wannier functions in the interior, and an unexpected one arising from net currents carried by Wannier functions near the surface. Each contribution can be expressed as a bulk property in terms of Bloch functions in a gauge-invariant way. Our expression is verified by comparing numerical tight-binding calculations for finite and periodic samples.

Orbital Magnetization in Extended Systems

While the orbital magnetic dipole moment of any finite sample is well-defined, it becomes ill-defined in the thermodynamic limit as a result of the unboundedness of the position operator. Effects due to surface currents and to bulk magnetization are not easily disentangled. The corresponding electrical problem, where surface charges and bulk polarization appear as entangled, was solved about a decade ago by the modern theory of polarization, based on a Berry phase. We follow a similar path here, making progress toward a bulk expression for the orbital magnetization in an insulator represented by a lattice-periodic Hamiltonian with broken time-reversal symmetry. We therefore limit ourselves to the case where the macroscopic (i.e. cell-averaged) magnetic field vanishes. We derive an expression for the contribution to the magnetization arising from the circulating currents internal to the bulk Wannier functions, and then transform to obtain a Brillouin zone integral involving the occupied Bloch orbitals. A version suitable for practical implementation in discretized reciprocal space is also derived, and the gauge invariance of both versions is explicitly shown. However, tests on a tight-binding model indicate the presence of additional edge currents, and it remains to be determined whether these can be related to the bulk band structure.

Thermal and solvent effects on the NMR and UV parameters of some bioreductive drugs

15N NMR chemical shifts and n-->pi* electronic transition energy for metronidazole (1) has been calculated and compared with experimental data. A detailed computational study of 1 is presented, with special attention to the performance of various theoretical methods for reproducing spectroscopic parameters in solution. The most sophisticated approach involves density functional based on the Car-Parrinello molecular dynamics simulations of 1 in aqueous solution (BP86 level) and averaging chemical shifts and deltaE(n-->pi*) over snapshots from the trajectory. In the NMR and UV calculations for these snapshots (performed at the B3LYP level), a small number of discrete water molecules are retained, and the remaining bulk solution effects are included via a polarizable continuum model (PCM). A good agreement with experiment is also obtained using static geometry optimization and NMR computation of pristine 1 employing a PCM approach. Further theoretical predictions are also reported for 17O NMR and deltaE(n-->pi*) of three hydroxycinnamic acid derivatives, which suggest that it is essential to incorporate the dynamics and solvent effects for NMR and UV calculations in the condensed phase.

Probing NMR parameters, structure and dynamics of 5-nitroimidazole derivatives. Density functional study of prototypical radiosensitizers

The 15N chemical shifts of metronidazole (1), secnidazole (2), nimorazole (3) and tinidazole (4), radiosensitizers based on the 5-nitroimidazole motif, are reported. A detailed computational study of 1 is presented, calling special attention to the performance of various theoretical methods in reproducing the 13C and 15N data observed in solution. The most sophisticated approach involves density functional-based Car-Parrinello molecular dynamics simulations (CPMD) of 1 in aqueous solution (BP86 level) and averaging chemical shifts over snapshots from the trajectory. In the NMR calculations for these snapshots (performed at the B3LYP level), a small number of discrete water molecules are retained, and the remaining bulk solution effects are included via a polarizable continuum model (PCM). A similarly good accord with experiment is obtained from much less involved, static geometry optimization and NMR computation of pristine 1 employing a PCM approach. Solvent effects on delta(15N), which are of the order of up to 20 ppm, are not due to changes in geometric parameters upon solvation, but arise from the direct response of the electronic wavefunction to the presence of the solvent, which can be represented by discrete molecules and/or the dielectric bulk.

Hydration of Y3+ ion: A Car-Parrinello molecular dynamics study

The solvation shell structure of Y3+ and the dynamics of the hydrated ion in an aqueous solution of 0.8 M YCl3 are studied in two conditions with and without an excess proton by using first principles molecular dynamics method. We find that the first solvation shell around Y3+ contains eight water molecules forming a square antiprism as expected from x-ray absorption near edge structure in both the conditions we examined. A detailed analysis relying upon localized orbitals reveals that the complexation of water molecules with yttrium cation leads to a substantial amount of charge redistribution particularly on the oxygen atoms, giving rise to the chemical shifts of approximately -20 ppm in 17O nuclear magnetic resonance relative to the computed nuclear shieldings of the bulk water.

Structural assignment of Diels-Alder adducts: an experimental and theoretical approach

A detailed NMR analysis with total assignment of (1)H and (13)C NMR data for the endo and the exo adducts, obtained by Diels-Alder reaction between 2-cyclohexenone and cyclopentadiene, is described. The unequivocal assignment of the endo and exo structures was performed by (1)H and (13)C NMR. These assignments were supported by theoretical chemical shift calculations at GIAO/HF level using 6-311 + g(2d, p) from optimized structures at the B3LYP/6-31g(d) level.

Solvent Effects on the UV (n → π*) and NMR (13C and 17O) Spectra of Acetone in Aqueous Solution. An Integrated Car−Parrinello and DFT/PCM Approach

The accurate reproduction of ultraviolet and nuclear magnetic resonance spectra of acetone in aqueous solution is used as a test of an integrated computational tool rooted in the density functional theory, the polarizable continuum model, and the Car-Parrinello dynamics. The analysis and solution of several conceptual and practical issues results in a robust and effective approach, which also can be used by nonspecialists and provides a general and powerful complement to experimental techniques.

Nuclear Magnetic Shielding and Quadrupole Coupling Tensors in Liquid Water: A Combined Molecular Dynamics Simulation and Quantum Chemical Study

Nuclear magnetic resonance (NMR) shielding tensors for the oxygen and hydrogen nuclei, as well as nuclear quadrupole coupling tensors for the oxygen and deuterium nuclei of water in the liquid and gaseous state, are calculated using Hartree-Fock and density functional theory methods, for snapshots sampled from Car-Parrinello molecular dynamics trajectories. Clusters representing local liquid structures and instantaneous configurations of a single molecule representing low-density gas are fed into a quantum chemical program for the calculation of the NMR tensors. The average isotropic and anisotropic tensorial properties of 400 samples in both states, averaged using a common Eckart coordinate frame, are calculated from the data. We report results for the gas-to-liquid chemical shifts of (17)O and (1)H nuclei, as well as the corresponding change in the nuclear quadrupole couplings of (17)O and (2)H. Full thermally averaged shielding and quadrupole coupling tensors are reported for the gaseous and liquid-state water, for the first time in the case of liquid. Electron correlation effects, the difference of classical vs quantum mechanical rovibrational averaging, and different methods of averaging anisotropic properties are discussed.

Proton transfer in heterocycle crystals

We study the proton diffusion process in imidazole-based molecular crystals, which are new candidate materials for fuel cell membranes. These materials are characterized by hydrogen bonded networks of molecules, which provide viable routes for the long-range diffusion of protons. By the application of a recently developed, powerful technique to determine reaction pathways in complex systems, we are able to reproduce the diffusion process in the imidazole crystal and in the more complicated and rigid structure of imidazole 2-ethyleneoxide. Our results cast new light on the atomistic details of the molecular rearrangements sustaining the ionic diffusion.

Supramolecular Assembly of Dendritic Polymers Elucidated by 1H and 13C Solid-State MAS NMR Spectroscopy

Advanced solid-state NMR methods under fast magic-angle spinning (MAS) are used to study the structure and dynamics of large supramolecular systems, which consist of a polymer backbone with dendritic side groups and self-assemble into a columnar structure. The NMR experiments are performed on as-synthesized samples, i.e., no isotopic enrichment is required. The analysis of (1)H NMR chemical-shift effects as well as dipolar (1)H-(1)H or (1)H-(13)C couplings provide site-specific insight into the local structure and the segmental dynamics, in particular, of phenyl rings and -CH(2)O- linking units within the dendrons. Relative changes of (1)H chemical shifts (of up to -3 ppm) serve as distance constraints and allow protons to be positioned relative to aromatic rings. Together with dipolar spinning sideband patterns, pi-pi packing phenomena and local order parameters (showing variations between 30% and 100%) are selectively and precisely determined, enabling the identification of the dendron cores as the structure-directing moieties within the supramolecular architecture. The study is carried out over a representative selection of systems which reflect characteristic differences, such as different polymer backbones, sizes of dendritic side groups, or length and flexibility of linking units. While the polymer backbone is found to have virtually no effect on the overall structure and properties, the systems are sensitively affected by changing the generation or the linkage of the dendrons. The results help to understand the self-assembly process of dendritic moieties and aid the chemical design of self-organizing molecular structures.

Benzoxazine oligomers: evidence for a helical structure from solid-state NMR spectroscopy and DFT-based dynamics and chemical shift calculations

A combination of molecular modeling, DFT calculations, and advanced solid-state NMR experiments is used to elucidate the supramolecular structure of a series of benzoxazine oligomers. Intramolecular hydrogen bonds are characterized and identified as the driving forces for ring-shape and helical conformations of trimeric and tetrameric units. In fast MAS (1)H NMR spectra, the resonances of the protons forming the hydrogen bonds can be assigned and used for validating and refining the structure by means of DFT-based geometry optimizations and (1)H chemical-shift calculations. Also supporting these proposed structures are homonuclear (1)H[bond](1)H double-quantum NMR spectra, which identify the local proton-proton proximities in each material. Additionally, quantitative (15)N[bond](1)H distance measurements obtained by analysis of dipolar spinning sideband patterns confirm the optimized geometry of the tetramer. These results clearly support the predicted helical geometry of the benzoxazine polymer. This geometry, in which the N...H...O and O...H...O hydrogen bonds are protected on the inside of the helix, can account for many of the exemplary chemical properties of the polybenzoxazine materials. The combination of advanced experimental solid-state NMR spectroscopy with computational geometry optimizations, total energy, and NMR spectra calculations is a powerful tool for structural analysis. Its results provide significantly more confidence than the individual measurements or calculations alone, in particular, because the microscopic structure of many disordered systems cannot be elucidated by means of conventional methods due to lack of long-range order.

Temperature-dependent hydrogen-bond geometry in liquid water

We have determined the hydrogen-bond geometry in liquid water from 0 to 80 degrees C by combining measurements of the proton magnetic shielding tensor with ab initio density functional calculations. The resulting moments of the distributions of hydrogen-bond length and angle are direct measures of thermal disorder in the hydrogen-bond network. These moments, and the distribution functions that can be reconstructed from them, impose quantitative constraints on structural models of liquid water.

Proton magnetic shielding tensor in liquid water

The nuclear magnetic shielding tensor is a sensitive probe of the local electronic environment, providing information about molecular structure and intermolecular interactions. The magnetic shielding tensor of the water proton has been determined in hexagonal ice, but in liquid water, where the tensor is isotropically averaged by rapid molecular tumbling, only the trace of the tensor has been measured. We report here the first determination of the proton shielding anisotropy in liquid water, which, when combined with chemical shift data, yields the principal shielding components parallel (sigma(parallel)) and perpendicular (sigma(perpendicular)) to the O-H bond. We obtained the shielding anisotropy sigma(parallel)-sigma(perpendicular) by measuring the proton spin relaxation rate as a function of magnetic induction field in a water sample where dipole-dipole couplings are suppressed by H/D isotope dilution. The temperature dependence of the shielding components, determined from 0 to 80 degrees C, reflects vibrational averaging over a distribution of instantaneous hydrogen-bond geometries in the liquid and thus contains unique information about the temperature-dependent structure of liquid water. The temperature dependence of the shielding anisotropy is found to be 4 times stronger than that of the isotropic shielding. We analyze the liquid water shielding components in the light of previous NMR and theoretical results for vapor and ice. We show that a simple two-state model of water structure fails to give a consistent interpretation of the shielding data and we argue that a more detailed analysis is needed that quantitatively relates the shielding components to hydrogen bond geometry.

Ab initio molecular dynamics with density functional theory

Recent applications of density functional theory base ab initio molecular dynamics in chemical relevant systems are reviewed. The emphasis is on the dynamical aspect in the study of structures, reaction mechanisms, and electronic properties in both the molecular and condensed phases. Examples were chosen from fluxional molecules, solution reactions, and biological systems to illustrate the broad potential applications and unique information that can be obtained from ab initio molecular dynamics calculations. Recent advances in the development of efficient numerical algorithms for the prediction of spectroscopic properties are highlighted.

The role and perspective of ab initio molecular dynamics in the study of biological systems

Ab initio molecular dynamics (MD) allows realistic simulations to be performed without adjustable parameters. In recent years, the technique has been used on an increasing number of applications to biochemical systems. Here we describe the principles on which ab initio MD is based. We focus on the most popular implementation, based on density functional theory and plane wave basis set. By a survey of recent applications, we show that despite the current limitations of size and time scale, ab initio MD (and hybrid ab initio MD/MM approaches) can play an important role for the modeling of biological systems. Finally, we provide a perspective for the advancement of methodological approaches which may further expand the scope of ab initio MD in biomolecular modeling.