Fundamental Intramolecular and Intermolecular Information from NMR in the Gas Phase

CYNTHIA J. JAMESON

University of Illinois at Chicago, USA Email: cjjames@uic.edu

1.1 Why Should One Do Gas Phase NMR Measurements?

In the gas phase we have a well-defined homogeneous physical system, and the theory for dilute gas behavior is in an advanced stage. In dilute gases, we can expand the molecular electronic property (e.g., nuclear magnetic shielding, J coupling, nuclear quadrupole coupling) in a virial expansion, in which the property virial coefficients can be expressed theoretically in closed form and can be obtained unequivocally experimentally in the binary interaction limit. These experimentally measured quantities depend on two quantum-mechanical mathematical surfaces: the shielding, or J, or electric field gradient (efg) at the nucleus as a function of intermolecular nuclear coordinates and the weak intermolecular interaction potential energy surfaces that are also a function of the same intermolecular nuclear coordinates. Furthermore, we can extrapolate the measured NMR data (shielding, J, efg) to the zero-density limit to obtain these electronic properties for the isolated molecule, that are much more closely related to quantum-mechanical calculations than quantities measured in condensed phases. To validate theoretical methods, it is always preferable to benchmark the results by comparing them with available experimental data, preferably for isolated molecules. Extrapolation to this limit is only possible for gas phase measurements. Here too, the temperature dependence of the electronic property at the zero-density limit is a function of two quantum-mechanical mathematical surfaces: the shielding (or J or efg) as a function of intramolecular nuclear coordinates and the intramolecular potential energy surface that are also a function of the same coordinates. The latter is commonly characterized by specifying the derivatives at the equilibrium intramolecular configuration, namely the quadratic, cubic, quartic force constants. The shielding is particularly sensitive to the anharmonicity of the intramolecular potential surface. Thus, gas phase NMR data for shielding, J, and efg provide stringent tests of theoretical descriptions of both the quantum-mechanical electronic property surfaces and also the potential energy surfaces over which they are averaged, to yield the temperature-dependent experimental data (property virial coefficients and zero-density limiting values) that are available only in the dilute gas phase. In addition to temperature, another variable, isotopic masses of neighboring (and observed) nuclei, can affect the measured data, given the same electronic property surfaces and the same potential energy surfaces; thus, isotope effects provide an independent test of these quantum-mechanical surfaces. While these observations and their interpretation are of specific interest to NMR spectroscopists, they are of more general interest as prototypes of rovibrational averaging and intermolecular effects on molecular electronic properties. Fortunately, it is possible in NMR spectroscopy to make very precise measurements of quantities that are very sensitive to changes in electronic environment, nuclear magnetic shielding and J, molecular electronic properties that are sensitive indices of the chemical bond and that vary with nuclear displacements from the equilibrium molecular configuration, leading to changes in resonance frequencies that are amenable to highly precise measurements under precisely controlled constant temperature conditions over a wide range of temperatures. Thus, gas phase measurements in NMR provide valuable tests of quantum-mechanically calculated molecular electronic property surfaces. Indeed, the dihedral-angle dependence of three-bond J coupling by Martin Karplus (known to NMR spectroscopists as the Karplus equation) was the earliest (1959) example of an experimentally testable quantum-mechanically calculated property surface. An important disadvantage of gas phase NMR, however, is that only the isotropic values of the NMR tensor quantities can be obtained.

For the same reasons, NMR spectra of dilute gases provide thermodynamic and kinetic information that are important from a theoretical point of view. The gas phase allows the separation of intramolecular and environmental effects on the energy requirements for molecular processes. Gas phase NMR data provide the free energy barriers for conformational changes, from which torsional parameters for molecular dynamics (MD) force fields are obtained. Furthermore, pressure can be used as an experimental variable in gas phase studies; rate constants are both temperature - and pressure-dependent. Use of dynamic gas phase NMR techniques permits the complete characterization of rate processes within both temperature and pressure ranges, allowing the kinetics of chemical rate processes to be investigated in both the unimolecular and bimolecular regimes. Information about internal vibrational redistribution and collisional energy transfer in kinetic processes is obtained from these NMR studies. Thus, conformational dynamics can be characterized under well-defined limiting conditions in the gas phase, free energy barriers can be obtained, and theoretical interpretation of results using well-established methods can provide detailed interpretation. A collateral experimental advantage is the rapid spin–lattice relaxation that facilitates multiple acquisitions; 13C relaxation times are at least two orders of magnitude shorter in the gas phase for some systems than in condensed phases. In the gas phase, we can measure spin–lattice relaxation rates that are of fundamental interest in their own right. The rates are resolvable into...