A new general technique for the investigation of exchange processes in molecular systems is proposed and demonstrated. Applications comprise the study of chemical exchange, of magnetization transfer by inter‐ and intramolecular relaxation in liquids, and of spin diffusion and cross‐relaxation processes in solids.

Investigation of exchange processes by two‐dimensional NMR spectroscopy

An empirical method to account for van der Waals interactions in practical calculations with the density functional theory (termed DFT-D) is tested for a wide variety of molecular complexes. As in previous schemes, the dispersive energy is described by damped interatomic potentials of the form C6R−6. The use of pure, gradient-corrected density functionals (BLYP and PBE), together with the resolution-of-the-identity (RI) approximation for the Coulomb operator, allows very efficient computations for large systems. Opposed to previous work, extended AO basis sets of polarized TZV or QZV quality are employed, which reduces the basis set superposition error to a negligible extend. By using a global scaling factor for the atomic C6 coefficients, the functional dependence of the results could be strongly reduced. The “double counting” of correlation effects for strongly bound complexes is found to be insignificant if steep damping functions are employed. The method is applied to a total of 29 complexes of atoms and small molecules (Ne, CH4, NH3, H2O, CH3F, N2, F2, formic acid, ethene, and ethine) with each other and with benzene, to benzene, naphthalene, pyrene, and coronene dimers, the naphthalene trimer, coronene · H2O and four H-bonded and stacked DNA base pairs (AT and GC). In almost all cases, very good agreement with reliable theoretical or experimental results for binding energies and intermolecular distances is obtained. For stacked aromatic systems and the important base pairs, the DFT-D-BLYP model seems to be even superior to standard MP2 treatments that systematically overbind. The good results obtained suggest the approach as a practical tool to describe the properties of many important van der Waals systems in chemistry. Furthermore, the DFT-D data may either be used to calibrate much simpler (e.g., force-field) potentials or the optimized structures can be used as input for more accurate ab initio calculations of the interaction energies. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 1463–1473, 2004

Accurate description of van der Waals complexes by density functional theory including empirical corrections

An ab initio gauge-invariant molecular orbital theory is developed for nuclear magnetic shielding. The molecular orbitals are written as linear combinations of gauge-invariant atomic orbitals, the wavefunctions in the presence of a uniform external magnetic field being determined by self-consistent field perturbation theory. The final magnetic shielding result is broken up into contributions which can be related to various features of electronic structure. Calculated magnetic shielding constants are presented using three sets of atomic orbitals, all of which are taken as contracted gaussian-type functions. The first two sets are minimal and the third is slightly extended. All three levels of theory give good descriptions of shielding at first row and hydrogen atoms. Carbon and hydrogen chemical shifts calculated at the extended level are in excellent agreement with experimental values.

Self-consistent perturbation theory of diamagnetism

Publisher Summary This chapter deals with the recent developments regarding the description and nature of the conformation of proteins and polypeptides with special reference to the stereochemical aspects of the problem. This chapter considers the parameters that are required for an adequate description of a polypeptide chain. This chapter focuses the attention on what may be called “internal parameters”—that is, those which can be defined in terms of the relationships among atoms or units that form the building blocks of the polypeptide chains. This chapter also provides an account of the mathematical method of utilizing these parameters for calculating the coordinates of all the atoms in a suitable frame of reference, so that all the interatomic distances, and bond angles, can be calculated and their consequences worked out. This chapter observes conformations in amino acids, peptides, polypeptides, and proteins.

Conformation of Polypeptides and Proteins

https://dspace.library.uu.nl/bitstream/handle/1874/24866/cullis_79_Lipid%20polymorphism.pdf;sequence=1

Lipid polymorphism and the functional roles of lipids in biological membranes.

Mathematical methods are presented for calculating rate constants of processes which narrow nuclear magnetic resonance absorption lines having discrete components. High resolution proton spectra show that the R1CO‐NR2R3 skeletons of N,N‐dimethylformamide (DMF) and N,N‐dimethylacetamide (DMA) are planar and suggest that N‐methylformamide, N‐methylacetamide, N‐methylformanilide and N‐methylacetanilide exist predominantly in one configuration. The presence of a significant amount of double bond character in the C–N amide bond is proved by the temperature dependent coalescence observed for the chemically shifted proton doublet of the N(CH3)2 groups in DMF and DMA, which gives values of about 22 and 19 kcal respectively for the free energy of activation required for reorientations about the bond.

Rate Processes and Nuclear Magnetic Resonance Spectra. II. Hindered Internal Rotation of Amides

Multiple magnetic resonance lines have been observed for H1, F19, and P31 nuclei in compounds such as PH3, PF3, F2PO(OH), and BrF5, in the liquid state. The multiplets consisted of two to seven equally spaced narrow components, symmetrically placed about a central frequency, and with splittings from 0.02 to 0.8 gauss. These multiplets arise from a new variety of interaction among the nuclear moments in a molecule. Resonance lines were found to be multiple either when a nucleus interacted with a different species of nucleus or when there was interaction between nuclei of the same species with resonance frequencies separated by a chemical shift. No compounds exhibited multiplets attributable to interactions among structurally equivalent nuclei. Nor were multiplets caused by nuclei whose electric quadrupole moments were coupled to a direction fixed in the molecule.The number and relative intensities of the components of a multiplet were determined by the number and statistical weights of the various nuclear spin orientations of the nuclei causing the splitting. In a given molecule, the ratio of the multiplet splittings of the two different resonance lines was inversely proportional to the ratio of the gyromagnetic ratios of the interacting nuclei. The splittings were independent of applied magnetic field at 4180 and 6365 gauss; they were independent of temperature over ranges from 55°C to −130°C. In PF5, the one gas examined, the splitting of the doublet fluorine resonance was the same in the gas and liquid phases; also, the doublet was demonstrated to arise from coupling with the phosphorus nucleus, rather than from a chemical shift between the resonances from the apex and meridian fluorines in the bipyramidal structure, as proposed earlier.All of the above characteristics are accounted for theoretically by assuming the magnetic nuclei interact via magnetic fields inside the molecule. The qualitative aspects are predicted by coupling of the form A12μ1·μ2 between the nuclear moments μ1 and μ2. The coupling constant A12 depends upon the detailed mechanism, which must involve the molecular electrons. Second‐order perturbation theory was used to calculate the relative magnitudes of coupling via the electron orbital and the electron spin magnetic moments. The electron spin mechanism was found to give splittings ten to twenty times the orbital. Approximate calculation of the electron spin mechanism in several simpler cases gave good agreement with experiment. The influence upon the splittings of electric quadrupole coupling and spin‐lattice relaxation was considered and is discussed briefly.

Nuclear Magnetic Resonance Multiplets in Liquids

The experimental absorption line widths, for nuclei with spin 1/2, at nuclear magnetic resonance are given as a function of temperature for a number of molecular crystals. Temperatures ranged from 90°K to the melting points of the compounds. In some cases it has been possible to relate observed line structure and transitions in the line width to the existence and frequency of certain types of hindered rotational motion in the solid state. These deductions are based on mathematical considerations of the quantitative effect of such motions on the structure and second moment of an absorption line. It is emphasized that relatively low frequency motion of the order 105 cycles/second suffices to narrow the width of an absorption line from its value in the absence of that motion.1,2‐dichloroethane, 1,1,1‐trichloroethane, and perfluoroethane were found to have line‐width transitions coinciding with changes in crystal form and anomalies in the heat capacity. In 1,2‐dichloroethane and perfluoroethane these transiti...

Structural Investigations by Means of Nuclear Magnetism. II. Hindered Rotation in Solids

We have studied the relaxation of conformers and the formation/relaxation of isomeric, weakly bonded dimers in pulsed supersonic expansions of seeded inert gases (He, Ne, Ar, Kr). The relaxation was determined from the intensity of a rotational transition for the higher energy species as a function of carrier gas composition, using the Balle/Flygare Fourier transform microwave spectrometer. Of thirteen molecules with rotational conformers which we examined, those with barriers to internal rotation greater than 400 cm−1 did not relax significantly in any of the carriers. The higher energy forms of ethyl formate, ethanol, and isopropanol, with smaller barriers, were not relaxed by He; those of ethanol and isopropanol were somewhat relaxed by Ne; and all were completely relaxed by as little as 5 to 20 mole percent of Ar or Kr in He or Ne. The relaxation in He or Ne is first order in the concentration of added Ne, Ar, or Kr as well as in the concentration of the high energy conformer. The pseudo first‐order r...

Relaxation of conformers and isomers in seeded supersonic jets of inert gases

The position of the proton magnetic resonance is concentration dependent in aqueous solutions of electrolytes yielding hydrogen containing ions. Chemical exchange averages the chemical shifts in the proton resonance position over the different chemical species. The averaged shifts observed are correlated with dissociation of the solute, and evidence is obtained in very concentrated solutions for the incomplete dissociation of HNO3, HClO4, and H2SO4 and for the formation of ion pairs of Na+OH−. A theoretical analysis of the relation between the magnetic absorption line shape and the chemical exchange frequency suggests that rather short chemical lifetimes can be measured; at least one can infer from the appearance of a single or complex resonance that the average lifetime is greater or less, respectively, than a determinable value in a range about 10−2 to 10−4 sec.

H. S. Gutowsky

Papers

Rate Processes and Nuclear Magnetic Resonance Spectra. II. Hindered Internal Rotation of Amides

Nuclear Magnetic Resonance Multiplets in Liquids

Structural Investigations by Means of Nuclear Magnetism. II. Hindered Rotation in Solids

Relaxation of conformers and isomers in seeded supersonic jets of inert gases

Dissociation, Chemical Exchange, and the Proton Magnetic Resonance in Some Aqueous Electrolytes