J . Phys. Chem. 1991, 95, 9788-9791
9788
Ab Initio Calculations and Experimental Measurement of the Deuterium Quadrupole Coupling Constant in Na,PDO, Jon D. Trudeau, Joe L.Schwartz, and Thomas C. Farrar* Department of Chemistry, University of Wisconsin-Madison, Madison, Wisconsin 53706 (Received: May 6, 1991)
The deuterium quadrupole coupling constant, xD, in the PDOj2-anion has been measured in solution by NMR spin-lattice (T,) relaxation time measurements and it has been calculated via ab initio methods. The experimental value of 94.7 f 0.5 kHz is in excellent agreement with the ab initio value of 95.0 kHz. The activation energy for the ion reorientation is 2.23 0.01 kJ mol-'.
*
spectral density functions have the form6
Introduction The work reported in this paper is part of a long-term effort in this laboratory to use a b initio calculations and experimental high-resolution NMR and N M R relaxation time measurements to learn more about molecular structure and dynamics in solution. These techniques provide a means to probe the molecular and electronic structure of a system by measuring or calculating values for the chemical shift, spin-spin coupling, dipolar coupling, and quadrupole coupling tensors for small molecules and ions. The goal in this and subsequent papers is to test the accuracy of a b initio calculations of quadrupole coupling constants and to understand in detail the nature and the magnitude of the solventsolute interactions which can cause changes in the electric field gradients. To this point, we have studied coupled two spins of one-half'S2 and systems with a single spin of I = Several preliminary studies of simple spin I-spin 1 /2 systems have been performed and further work is in progress. In this paper, temperature-dependent data for the relaxation of the deuterium nucleus in PD0,2- is presented. Deuterium is a spin 1 nucleus and therefore has a nuclear quadrupole moment. Although this system is a coupled two-spin system (spin 1-spin 1 /2), the deuterium quadrupole interaction is about 30 times greater than either the CSA (chemical shift anisotropy) or the dipole-dipole interaction and its contribution to the total relaxation rate is consequently about 1000 times greater. For this reason and reasons presented below, we consider here only the effects of the quadrupole interaction. Until recently it has usually been assumed that, for a particular compound in solution, the quadrupole coupling constant of a spin 1 nucleus is independent of the solvent. Recent work?v4 however, has shown that the quadrupole coupling constant for both nitrogen-I4 and deuterium can change appreciably as a function of solvent. It is therefore important to understand what intermolecular and intramolecular interactions affect the quadrupole coupling constant and to be able to predict with reasonable accuracy the values of the quadrupole coupling constant. The measurement of deuterium relaxation times is of considerable interest since protons are commonly found in molecules of chemical and biochemical interest. Deuteration of a particular site in a system of interest provides a way to obtain information about the local environment and molecular dynamics.
Theory The relaxation rate of an isolated spin I = 1 nucleus, is given by5 R , = l/T1= (3/40)x2{J(o) + 4J(2w)) (1) where x = [eQq/h]is the quadrupole coupling constant expressed in rad/s, eQ is the electric quadrupole moment, q = a2V/az2is the electric field gradient at the nucleus, 0 is the nuclear Larmor frequency in rad/s, J ( w ) and J(2w) are spectral density functions (given below), and rc is the molecular correlation time for isotropic reorientation. For isotropic Brownian diffusional motion these *Author to whom correspondence should be sent.
0022-3654/9 112095-9788$02.50/0
J(w) = J(2w) =
TC
1
+
w27,2 'TC
1
+ 4w27f2
In the extreme narrowing region (i.e., wrc
