Extended Townes-Dailey Analysis II: Application to hybridized orbitals Columbus, 2010 TC 01 Nuclear Quadrupole Coupling Constants Stewart Novick Wesleyan University

Quick review of last year’s talk: unhybridized orbitals:

The point here is that the electric field gradient at a nucleus is dominated by the p-electrons on that atom. Electric field gradients at a nucleus due to various hydrogenic electrons 1

HGeBr, L. Kang, F. Sunahori, A.J. Minei, D.J. Clouthier, S.E. Novick, JCP 130, (2009) D 74 Ge 79 Br χ aa ( 79 Br) = (1) MHz χ bb ( 79 Br) = (3) MHz χ cc ( 79 Br) = (3) MHz D 73 Ge 79 Br χ aa ( 73 Ge) = 8.641(16) MHz χ bb ( 73 Ge) = 220.(21) MHz χ cc ( 73 Ge) = -229.(21) MHz 17 isotopologues of HGeBr have been studied by FTMW spectroscopy. A total of 711 microwave transitions have been measured and assigned. Some nuclear quadrupole coupling tensor elements. Notice that the b and c elements at bromine are very different! c

Modeling the hyperfine constants In a standard Townes-Dailey analysis, n b and n c are set equal to 2 and n a is solved to fit only χ aa. n a = 1.58, n b = 2.00, n c = 1.80 J.G. King, V. Jaccarino, Phys. Rev. 94, 1610 (1954).

Generalize to hybridized orbitals, sp 3 f1f1 f2f2 f3f3 f4f4

creation of the four Q matrices These integrals are done in Mathematica To scale these to the values of the quadrupole coupling constants for a single p-electron of a nitrogen atom, multiple by 30 a 0 3  0, where  0 is an experimentally determined constant.

X 0 = MHz, note sign lone pair bonding to hydrogens bonding to carbon check: rotation by 120 o about z interchanges the last three matrices

lone pair bonding to hydrogens bonding to carbon X 0 = MHz Considering only the diagonal elements, there are two independent equations, but there are three independent unknowns n 1, n 2 = n 3 by symmetry of methylamine, and n 4. The equations are underdetermined. If we assume that there are 2 electrons in the lone pair (n 1 = 2), then n 2 + n 1 = 2.91, and n 4 = xz element (if you believe X xz = 0) gives n 4 = (n 2 +n 3 )/2, which is approximately correct in all cases. X xy = 0 and X yz = 0 are obeyed identically 22n 1 (lone pair) (n 2 +n 3 ) (to H) n 4 (to C) covalent 8 ionic nominal max STO-3G ?? total

sp 2 orbitals 1,2-dihydro-1,2-azaborine A.M. Daly, C. Tanjaroon, A.J.V. Marwitz, S.-Y. Liu, S.G. Kukolich, JACS 132, 5501 (2010) x y z out-of-plane g 1 points along the N-H bond g 2 points along the N-C bond g 3 points along the N-B bond 2p z points out of the plane g1g1

experimental to H to C to B p z n pz g1g1 nHnH g 2 +g 3 n C + n B n total about N Again, two equations and three unknowns. There is no way to distinguish between populations of the sp 2 orbital to C and to B without  xy. Setting n pz and calculating the other populations we obtain: The two blue columns are the most reasonable (charge on N or -0.67). Kukolich states n pz = 1.6 from MP2/6-311+G(d,p) NBO calculation. STO-3G

sp hybridization H 3 C–C≡N, methyl cyanide, G. Winnewisser & coworkers, JMSp 226,123 (2004) experimental to carbon lone pair p x p y nominalSTO-3G h 1 +h pxpx pypy total two equations three unknowns there are no off-diagonal tensor components

Acknowledgements Stephen Kukolich, University of Arizona Dennis Clouthier, University of Kentucky Pete Pringle, Wesleyan University Dan Frohman, Wesleyan University Bob Bohn, University of Connecticut

THE END

Acknowledgements Collaborators and group members – Lu Kang, Southern Polytechnic State University, Marietta, Georgia – Wei Lin, University of Texas at Brownsville, Texas – Pete Pringle, Wesleyan – Andrea Minei, PhD 2009, Wesleyan – Dan Frohman, Graduate Student Wesleyan – Jovan Gayle ‘07, Wesleyan – William Ndugire ‘10, Wesleyan – Ross Firestone ‘12, Wesleyan – Chinh Duong ’13, Wesleyan – Jennifer van Wijngaarden, University of Manitoba – Bob Bohn, University of Connecticut – Karen Peterson, San Diego State University – Tom Blake, Pacific Northwest National Laboratory – Dennis Clouthier, University of Kentucky Special Thanks – Jens Grabow, University of Hannover, ftmw++ – Herb Pickett, Jet Propulsion Laboratory, retired; Visiting Scholar, Wesleyan University, SPCAT / SPFIT – Mike McCarthy & Pat Thaddeus, Harvard Smithsonian Center for Astrophysics

For 73 Ge, χ 0 is +224 MHz for one 4p electron. A similar p-population analysis for the 73 Ge nuclear quadrupole tensor of D 73 Ge 79 Br yields n a = 0.71, n b = 1.34, and n c = Br Ge n p (Ge) = 2.05n p (Br) = 5.38 np(total) = 7.43, “should” be 7 Implies 38% ionic character. “Standard” T-D analysis gives 58%. Electronegativity differences estimates 20% ionic character for this Bond.

How does this compare with theory? Townes- Dailey STO-3Gaug-cc- pVTZ Ge n a n b n c # p-electrons Br n a n b n c # p-electrons Bottom line: The non-cylindrical symmetry of the χ tensor is a reflection of the p-electron populations