2999
CRYSTAL LATTICEEFFECTS IN THE NQRSPECTRA
Crystal Lattice Effects in the Nuclear Quadrupole Resonance Spectra of Some Hexachlorostannate(1V) Saltsla by T. B. BriI1,lb Z Z. Hugus, Jr., and A. F. Schreiner Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27607
(Received February 2 , 1970)
The 35Cl and some 3’Cl nqr spectra in ten different salts of SnC1,2- have been recorded and the resonance frequency trends due to the lattice interpreted. When the anion-cation covalency was expected to be variable, the electrostatic point charge model failed t o explain the observed trends. I n compounds containing nearly constant-anion cation convalency, explanation of the trends using the point-charge model was reasonably successful. Differences in the crystal lattice induced up to a 10% variation in the 35Cl resonance frequency. Use of an empirical lattice Sternheimer antishielding factor of 10 for chlorine is consistent with the results. Semiempirical LCAO-h!tO calculations were carried out on SnC162- and TeCb*-, and computational verification for the ‘‘inert pair effect” was obtained.
Introduction An important problem in nqr spectroscopy is the understanding of how much the nqr frequency of an atom in a chemical moiety can be affected by the crystal lattice surrounding it. I t is the purpose of this paper to report the effects of a variety of cations on the Wl and some 3’Cl resonance frequencies in the hexachlorostannate(1V) ion, SnC16z-. I n the absence of good crystal wave functions, approximate models were used in order to interpret the results. An attempt is therefore made to account for the trends rather than the absolute frequencies.
Experimental Section Chloride salts of the cations (AR Grade) were added stoichiometrically to dilute HCl solutions containing known amounts of SnCl4.5Hz0(AR Grade). The solutions were allowed to evaporate from one to four weeks. I n most cases, large well-formed crystals grew. For several compounds, notably the Rb+, Cs+, and (CH8)2J+salts, only small crystals were obtained. The nqr spectra reported inTable Iwere recorded using a Wilks Scientific NQR-1A nuclear quadrupole resonance spectrometer. A Hewlett-Packard 5245L electronic counter mas used for frequency measurements. Only one 35Clresonance frequency was found in each compound studied but because a superregenerative oscillator-detector was used, the possibility of two very closely spaced resonances cannot be ruled out. Attempts were made to record the resonance frequencies of about twenty additional compounds, but their spectra could not be detected a t room temperature using our spectrometer,
Calculations Lattice electric field gradient (EFG) was computed using a general point charge lattice summation computer program. The elements, q l j , of the symmetric
tensor a t a point, such as at a nucleus, due to a charge, ek, a distance r away are given byz
(””)
qfj = bx&j
(3xixj rso =
CekCC k i j
- 8ijr2) r5
(11
V is the electrostatic potential a t the nucleus, and xi,x5 are the Cartesian coordinates x, y, and x . = 1 if i = j and 0 otherwise. By scanning all charges in a spherical volume of a chosen radius and by computing six of the nine qlJ’s for each, the lattice EFG tensor was generated. Diagonalization of the tensor yields the eigenvalues of the principal axes, which are converted to MHz, along with their eigenvectors relative to the initial axes. The eigenvalues must be corrected for the Sternheimer antishielding e f f e ~ t . ~ Burns and Wikner4 have suggested an empirical multiplicative factor of 10 for 36Cl.5 This value appears to be very reasonable based on the results presented herein and will be discussed. I n order to obtain the self-consistent charges and intramolecular EFG in the SnCla2- ion, an LCAO-MO calculation was carried out. The same type of calculation was also performed on TeCla2- for purposes of comparison. An extensively modified SCCC-MO-like program based on Hoffmann’s6 was used. I n this (1) (a) Abstracted from the thesis of T. B. B. submitted to the Graduate School of the University of Minnesota in partial fulfillment of a Doctor of Philosophy degree. (b) NDEA predoctoral fellow a t the University of Minnesota, 1966-1969. Address inquiries t o Department of Chemistry, University of Delaware, Newark, Del. 19711. (2) A. Abragam, “The Principles of Nuclear Magnetism,” Oxford University Press, New York, N. Y., 1961. (3) R. M.Sternheimer and H. M. Foley, Phys. Rev., 102, 731 (1956), and references therein. (4) G. Burns and E. G. Wikner, ibid., 121, 155 (1961). (5) The Sternheimer antishielding factor is defined as (1 - y,J, We have thus chosen y m = -9. (6) R. Hoffmann and W. N. Lipscomb, J . Chern. Phys., 36, 2179 (1962).
The Journal of Physical Chemistry, Val. 74, No. 16, 1970
3000
T. R. BRILL,2 Z. HUOUS, JR.,AND A. F. SCHREINER
Table I : a6C1 and a7Cl Nqr Frequencies (MHz) for SnClez- Salts of Various Cations“
15.064 i:0.003 15.60 i O . 0 2 16.05 i 0 . 0 5 15.835 i 0.003 15.752 i 0.003 15.708 i 0.003 15.475i0.003 15.811=tO0.O03 16.635f0.003 16.663 f 0.003
12: 1 2: 1 2: 1 9: 1 5: 1 30: 1 3: 1 25: 1 15: 1 4: 1
11.87OiC0.003
... ...
6: 1
... ...
12.478 i 0.003 12.411 i 0.003 1 2 . 3 8 0 i 0.003
3: 1 2: 1 7: 1
12.460 i:0.003 13.109i0.003 13.127 i:0.003
6: 1 5: 1 2: 1
...
...
30.128 f 0.006 31.20 i 0 . 0 4 32.10 iC0.10 31.670f0.006 31.504f0.006 31.416 i 0.006 30.950f 0.006 31.622f 0.006 33.270 f 0.006 33.326 i 0.006
a All resonance frequencies were recorded at 23’. D. Nakamura, Bull. Chem. Soc. Jap., 36, 1162 (1963) ( W l resonance only.) The coupling constant was taken to be twice the resonance frequency. In the cases of the K+, Rb+, Cs+, NH4+, and (CHa)qN+ salts, this is exactly correct based on crystallographic data. In the others the lattice will probably generate a small asymmetry parameter in the EFG. However, even in the unlikely circumstance that the asymmetry parameter is as large as 0.1, this approximation still represents less than 0.2% error in the coupling constant. 0
computational procedure the diagonal Hamiltonian matrix elements, Hit,of the metal were approximated as valence orbital ionization potentials’ with all orbital energies derived from atomic spectral data in Moore’s tables.* They were charge adjusted by -3.5 eV per unit charge. The analytical, single term, Slater-type metal orbital exponents were derived by fitting their shape in the overlap region to Herman-Skillman selfconsistent field (SCF) wave functionsag Clementi-Raimondi’O functions were used for chlyine. Bond distances of 2.43 A in SnCl&- and 2.54 A in TeClG2-were employed for these overlap integral It became apparent that the metal 4d orbital is not very important in bonding, since it is very contracted, of low energy, and therefore completely filled in these complexes. In fact, the valence bond approach suggests the use of metal 5d orbitals by forming sp3d2hybrids. Therefore, the tin 5d orbitals were employed. The exponents were generated by determining the maximum overlap with the chlorine orbitals and then contracting them due to the atom positive charge by 0.2(Sn) and 0.3(Te) unit. The magnitude of these contractions is in line with similar results obtained by Richardson, et aZ.13 The 4d orbital was then neglected. Off-diagonal Hamiltonian matrix elements, H t j , were calculated by the Wolfsberg-Helmholz method14
Hij
=
0.5KSaj(Htt
+
Hjj)
(2)
where Xtj is the overlap integral between the ithand jth functions. K is a constant set equal to 1.75. Cusachs’ methodI5 for computing H , j was also investigated. It led to substantially the same EFG as (2) but slightly larger charges resulted on the metal and chlorine atoms. The approximation was abandoned since small, but not negligible, negative orbital occupations resulted in the metal e, orbitals. Input orbital exponents and Coulomb integrals are listed in Table 11. Self-consistent output charges and The Journal of Physical Chemistry, Vol. 74, No. 16,1970
orbital occupations are listed in Table 111. Substitution of chlorine p orbital “holes”, U (obtained from 2-orbital occupations) into the following equation yields the 36Clnuclear quadrupole coupling constant for the molecular ion in MHz. The approach that Cotton (e2&q/h) = -109.7
+2 ”.>
Table I1 : Input’Molecular Orbital Parameters for SnClS2-and TeCls2-
Orbital type
Slater-type orbital exponents,a (2
2.15 1.65 1.38 2.25 1.89 1.50 2.356 2.039
Hi
