854
HAROLD BASCHAND A. P, GINSBERG
A Molecular Orbital Description of TcHg2by Harold
Baschl
and A. P. Ginsberg
Bell Telephone Laboratories, Inc., Murray Hill, New Jersey
(Received July 82. 1 9 6 8 )
A ground-state molecular orbital wave function has been calculated for the TcHg2- ion within the full, nonempirical Hartree-Fock-Roothaan formalism in a large gaussian orbital basis. The computed M0's are used to calculate net charges on the atoms, the absolute magnetic shielding at the protons, and the anisotropy in the strictly diamagnetic part of the bulk susceptibility. The calculated shielding is in satisfactory agreement with the experimental value. It is concluded that the hydrogens in TcHg2- are almost identical in regard
to their electronic environment. The lowest lying band positions, polarizations, and intensities in the electronic absorption spectrum are estimated.
A hydrogen atom bonded directly to a transition metal atom or ion is noted for its high-field proton magnetic shielding constant.2 We have used this experimental information to test the feasibility of obtaining a molecular orbital description of a metal hydride within the framework of the nonenipirical molecular orbital theory, by calculating the ground and also certain excited electronic states and structural properties of the formally do TcHg2- ion. The Roothaan SCF-MO f0rmalisrn3~ in a contracted (single-!: for the core and double!: for the valence shell AO's) gaussian orbital basisabwas used. It should be noted that the calculational procedure contains no adjustable parameters, includes all electrons, and requires the evaluation of all (in this case -20 million) integrals. Integral evaluation time was about 4 hr on a GE 645 computer. For a closed-shell electronic configuration the computational procedure is perfectly straightforward, requiring only the choice of basis set and geometry. K2TcHg is isostructural with KzReHgand has a unit cell volume only 1.7% greater than that of K2ReHga4We have therefore assumed that the TcHg2- ion has the same structure as has been found for ReHg2- (point group Dah symmetry) by a neutron diffraction study.6 The structure is shown in Figure 1; a uniform Tc-H bond distance of 1.70 A, slightly larger than the value of 1.69 A found for ReHg2-, was used. The angle between hydrogens in the same vertical mirror plane was taken as 93.6', the same as in ReHg2-. The T c basis set was obtained by first optimizing6 all exponents in a 1lS8p7d gaussian primitive-orbital basis' for a T c ~ 4d6 + configuration. The resulting COefficients and exponents were then used to construct the contracted basis set shown in Table I. The 5s and 5p atomic orbitals were obtained by scaling the Slater orbital basis atomic SCF calculation for molybdenum of Roothaan and SynekS8 For the H atoms a 48 f i t 9 to a Slater Is exponent of -0.9 was split into three-term and one-term sets of basis functions designated 1s and ls'in Table I. Note that the 4d A 0 has The Journal o j Physical Chemistry
also been split into a 4d and a 4d' orbital to allow greater variational freedom in the calculation away from the arbitrary choice of charge and configuration in the basis set and in an effort to minimize the basis set dependence of the computed results. The computed ground-state MO's have been used to calculate net charges on the atoms via a Mulliken population analysis, the absolute magnetic shielding a t the protons, and the anisotropy in the strictly diamagnetic part of the bulk susceptibility. Also, the positions of the lowest excited electronic states in the optical spectrum and their polarizations and intensities have been estimated. The isotropic values for the absolute shielding at the protons were calculated from UIi
= 3-1C-2[(*~
I YH-' I * O ) -
Rq(*O
1 qH/rHa I *0)]
9
(1) where 3 - k 2 = 17.7497 X lov6, q = x, y, z, is the computed ground-state wave function, the integrals are in atomic units, and the proton is at a distance R = dC,R," = 1.70 A from the Tc atom. This formula has been discussed el~ewhere"J-'~ and is considered fully applicable to the proton shielding in TcHg2-. The results of this investigation offer further evidence for the validity of (1) in these situation^.'^
*O
(1) Ford Scientific Laboratory, Dearborn, Mich. 48121. (2) For recent reviews see A. P. Ginsberg, T r a n s i t i o n Metal Chem., 1, 111 (1965); M. L. H. Green and D. J. Jones, A d v a n . Inorg. Chem. Radiochem., 7, 115 (1965). (3) (a) C. 0. J. Roothaan, Rev. M o d . Phys., 23, 69 (1951); (b) H. Basch, C. Hollister, and J. W. Moskowitz, Abstracts, 154th National Meeting of the American Chemical Society, Chicago, 111. 1967, No. 081. (4) A. P. Ginsberg, I n o r g . Chem.. 3, 567 (1964). ( 5 ) 5 . C. Abrahams, A. P. Ginsberg, and K. Knox, ibdd., 3, 558 (1964). (6) The atomic SCF computer program was kindly supplied by Dr. 0. J. Hornback. (7) l l s = 11 s-type gaussian primitive orbitals [radial dependence N e x p ( - a r 2 ) ] , etc. For a discussion of primitive Z.S. contracted functions, see J. M. Schulman, J. W. Moskowitz, and 0. Hollister, J. Chem. Phys., 46, 2759 (1967). (8) C. C. J. Roothaan and M. Synek. Phys. Rev., 133, A1263 (1964). (9) S. Huainaga, J. Chem. Phys., 42, 1293 (1965).
855
A MOLECULAR ORBITALDESCRIPTION OF T c H F
Figure 1. Perspective arrangement of hydrogen atoms in TcHg2-, based on the known structure of ReHS2-.
The first term in (1) is the average diamagnetic part of the shielding constant and for one of the The equatorial protons amounts to +295.2 X second term is part of the ordinary paramagnetic shielding term, extracted from the usual sum over
Table I: Gaussian Orbital Basis Set" Basis function*
A0
Tc 18
+ + + + + + + + + + + +
+
2s 3s 4s 58 2P" 3PC
4PC 5PC
3dd 4dd 4dId
+
0.006461 (59,660) 0.046997 (8920) 0.213133 (2049) 0.508622 (562.4) 0,351552 (197.5) 0.729331 (45.73) 0.409957 (18.82) 0.782913 (7.168) 0,530820 (3.570) 0.723624 (1.50) 0.630291 (0.5250) 0.534250 (0.1035) 0.599810 (0.03242) 0.029791 (1113) 0.190172 (266.4) 0.496210 (84.56) 0,404304 (31.96) 0.492456 (12.11) 0.578946 (4.990) 0.4400 (2.066) 4- 0.781378 (0.6768) 0.534250 (0.1885) 0.599810 (0,05901) 0.091822 (85.41) 0.362753 (24.86) 0.549056 (8.625) 0.250134 (2.967) 0.077886 (2.967) 0.423549 (1.271) 0.448769 (0.5299) 1.000000 (0.2078)
+
+
la'
where the prefactor is evaluated as 0.791998 X cgs/g-atom, the integral is in atomic units, and the origin of q is taken a t the center of mass or center of electronic charge,12 which happen t o coincide at the
+
+
0.019060 (10.69) 0.134240 (1.611) (0.3630) 1.OOOOOO (0.09865)
(10) C. W. Kern and W. N.Lipscomb, J. Chem. Phys.,37, 260 (1962). (11) R. M . Stevens, 0. W. Kern, and W. N. Lipscomb, %'bid., 37, 279 (1962).
+ 0.474490
a The contracted Tc atom basis set is comparable to a minimal Slater orbital basis except for the d's which are probably somewhat better. *The functions are tabulated in the form Cl(a1) C Z ( ~ Z ) . . , where the C's are the coefficients and the a ' s are the gaussian exponents. Each of type 2, y, and 3, with radial dependEach of type xy, zz, yz, x 2 - y2, and 2z2 ence N r exp(-ar2). x 2 - y2, with radial dependence -9 exp(--orr2).
+ .
+
+
H Is
excited states14 by a coordinate transformation on the angular momentum operator. For the same proton this second term contributes -251.5 X for a net For a proton at one absolute shielding of 43.7 X of the apices of the trigonal prism the corresponding values are (+295.6 - 250.9) X low6= 44.7 X E~perirnentally,~ TcHg2- in solution shows only a single proton nmr absorption at T 18.4 ppm which corresponds to an experimental absolute shielding of 39.0 X 10-6.16 Thus the high-field proton magnetic shielding constant is satisfactorily obtained from the computed MO's. Table I1 presents a population analysis breakdown of the valence shell MO's and the individual MO contributions t o the UH values quoted above. The core (Tc Is, 2s, 2p, 3s, 3p, 3d, 4s' 4p) electrons contribute nothing to the shielding as can be predicted from eq 1 by considering the core functions as point charges; r H - l goes to R-' and RqqH/rHaalso goes t o R-I. Previous authors"J4 have tried to pinpoint the origin of, or largest oontributions to, the chemical shift, but the very mixed metal ligand character of these MO's precludes such an analysis here. Interestingly enough, a total population analysis predicts that each equatorial proton carries only a rather small excessive negative charge (-0,139). The corresponding value in the apical positions is -0.203. As expected, the slightly larger negative charge correlates with the slightly larger shielding constant. Previous investigators'e have found that charges roughly twice as large as those obtained here were also able to explain the analogous high-field chemical shift in R e H P , which is only 0.7 ppm greater than in TcHg2-. The average value of the diamagnetic contribution to the bulk magnetic susceptibility can be obtained from12
+
(12) 5. I. Chan and T. P. Das, i b i d . , 37, 1527 (1962). (13) A. D. Buckingham and P. J. Stephens, J. Chem. Soc., 2747 (1964). (14) W. N. Lipscomb, Advan. Magn. Resonance, 2 , 137 (1967). (15) From W. H . Flygare, J. M. Pochan, G. I. Kerley, T. Caves, hI. Karplus, S. Aung, R. M. Pitzer, and S. I. Chan, J. Chem. P h y s . , 45, 2793 (1966); UTMS U H ~ O ( ~=) $0.6 X U H ~ O ( . ) - UH% = 3.4 X 10-8, and U H ~= 26.6 X 10-6, yielding UTMS = 30.6 X 10-6. Therex 10-6 8 . 4 x 1 0 - 8 = 39.0 x 10-8. fore U T ~ H ~=~ 30.6 (16) L. L. Lohr, Jr., and W. N. Lipscomb, Inorg. Chem., 3, 22 (1964). These authors quote experimental u values that are consistently -4.0 X 10-6 higher than what would be derived using UTMS = 30.6 X 10-8 16 and the experimental chemical shifts on the
-
+
T
scale.*
Volume 79,Number 4 April 1869
HAROLD BASCHAND A. P. GINSBERG
856
Table 11: Valence Shell MO’s in TcH82Population analysisb Tc (5s)
Symmetrya
--Magnetic
H ( 1 ~ ) ~ Tc (4d)f
0.775 0.47 0.47 0.54 0.54 0.38 0.83 0.72 0.72 0.70 0.695 0.52
681’
2e” (xz) 2e” (yz) 5e’ ( 2 2 - y2) 5e’ (XY) 7al’ (222 - x 2 - y*) 4aP 6e’ ( x 2 - y2) 6e’ (XY) 8a1‘ (222 - 2’ - Ya) 7e’ (x3- y2,xy) 3e” (xz,yz)
Tc ( 5 ~ )
0.225 0.53 0.53 0.42 0.42 0.62
BEd
6.1 2.3 3.4 11.8 2.1 4.5 4.3 4.9 4.3
0.04 (x) 0.04 (Y) 0.17 ( z ) 0.12 (5) 0.12 (Y)
0.16 0.16 0.30 0.305 0.48
shieldin@--
BEC
6.1 5.7 2.6 2.5 3.6 2.6 8.1 10.0 3.5
1 + 5a’, 1 + 3Q”, 1 4e’, and le” constitute the core. 8a’, 7e’, and 3e” are not occupied. The MO’s are listed in order of increasing orbital energy. Normalized t o one electron per MO. Absolute shielding for H(8) in Figure 1 using eq 1. Absolute shielding for H(l) in Figure 1 using eq 1. 6 Sum of 1s and 1s’ populations. f Sum of 4d and 4d’ populations. 0 In ppm.
*
Table 111: Lowest Lying Allowed Electronic Transitions in TcHs2Upper state (polarization)
One-electron excitation
A Ea
-ER~
6e’ 3 Sal’ 7al’ -+7e’ 6e’ --t 7e’ 4aL’ -+ Sal’
0.51591 0.55005 0.52194 0.54098
-0.25013 -0.25549
( $ 1 Y) ]E’ (2,$9
lE’
lE’ (2,Y) ‘Az” (I) a
Orbital energy difference (in m).
b
-
The Journal of Physical Chemistry
Oscillator strengthd
7.23 8.01 9.56 9-00
0.008 0.413 0 482 0.470
-0.17060 -0.21019
Sum of electron repulsion energy terms (In au).
Tc atom in TcHg2-. Since we are not able to obtain the paramagnetic only part of the susceptibility, of greater interest is the anisotropy in x d defined as (xdlS x d Z Z ) / x d Z Ewe . compute^^,, = -57.86 X cgsu and xdZZ ( = xdYnl)= -54.49 X cgsu, for a rather small anisotropy of about 6%. A population analysis of the metal valence shell orbitals yields the electronic distribution 4d6.6g85s0.6325p1.276 with the 4d electrons rather uniformly distributed among the 5 orthogonal d orbitals, and the p electrons equally allotted to the 5pZ,5p,, and 5p, orbitals. These data, combined with the previous information that both the net charges and proton chemical shifts are very similar for the equatorial and apical protons, support the assertion6 that the hydrogens in TcHg2- are nearly equivalent with regard to their electronic environment. Thus in the solid, where rapid interchange of the protons does not take place, these calculations predict that the two proton nmr absorptions expected for TcHs2- will be very close to each other. I n the virtual orbital approximation and neglecting spin-orbit coupling effects, vertical electronic excitation energies can be obtained from the computed occupied and unoccupied MO’s shown in Table 11. There is no direct experimental evidence on the electronic absorption spectrum of TcH92-, but the isostructural ReHg2- ion in solution shows a single maximum below
Excitation energyC
c
In eV.
I
See text.
50,000 cm-l at 5.9 eV ( f M 0.03) which has been assigned as an c’ + all transition.6 In going from Re to Tc in the same oxidation state we would expect the excitation energy to red-shift slightly. The four lowest lying spin and electric dipole allowed excited states corresponding to one-electron excitations from occupied to unoccupied MO’s in Table I1 and their oscillator strengths are shown in Table 111. The formulas for deriving the excitation energies are obtained in the standard wayas and each involves an orbital energy difference ( Ae) plus electron repulsion energy terms ( -En), individually tabulated in Table 111. Oscillator strengths have been calculated from a mixed dipole velocity-dipole length expression which eliminates the excitation energy from appearing explicitly in the intensity ~ a l c u l a t i o n . ~ ~ From Table I11 it is clear that the lowest lying allowed transition is of 2 , y polarization, corresponding to the excitation of an electron from the 6e‘ to the Sal‘ MO. Although the computed excitation energy is apparently too high (by -1.5 eV) and the intensity is too low, configuration mixing with the other nearby lE’ states which have large oscillator strengths is sure to improve both the computed position and the intensity (especially the latter) of the first allowed tran(17) A. E.
Hansen, Mol. Phys., 13, 425 (1967).
PMRSTUDY OF H20-NH3 PROTON EXCHANGE sition. The first z-polarized transition (lAz”) is expected to be well separated from the first lE’. This is a reasonably good accounting of the expected electronic absorption spectrum of TcHg2-, its predicted onset at rather high energies correlating with the observed spectrum of ReHg2-.
857
Acknowledgments. The authors wish to thank Dr. David B. Neumann for many interesting and informative discussions on properties, Dr. Charles Hornback for the use of his atomic SCF program, and Dr. M. B. Robin for clarifying discussions on ligand field spectra.
Proton Magnetic Resonance Study of Water-Ammonia Proton Exchange in Water-Ammonia Solutions Containing Added Potassium Hydroxide 1 by Mohammed Alei, Jr., and Alan E. Florin University of California, Los Alamos Scientific Laboratory, Los Alamos, New Mesico
87544
(Received July 2 9 , 1 9 6 8 )
The exchange of protons between H20 and NH3 in solutions of BzOin liquid NH3 at 29.6 A 0.2’ is accelerated by addition of OH-. The overall kinetics for Hz0 concentrations from 1 to 12 M and added [OH-] from zero to -2 X loM3M is well represented by rate = kl[OH-]+ k2[0H-][Hz0]2 k3[NH41-][H20] k4[HzO]4 with kl = 7.4 X lo4 sec-l, kz = 0.84 X lo4 sec-l M-2, k3 = 3.48 X lo6 s e r l M-l, and kc = 0.058 set" A t the highest He0 concentrations, the effect of the third term in the above rate expression allows one to place Thus at 12.2 M HzO,K,,,,, = [NH*+][OH-]/ rather narrow limits on the ionization of Hz0 in liquid “3. and at 9.05 M H20, Kim = (1.1 j=0.1) X lo-”. The remaining terms in the [HzO] = (3.9 A 0.3) X rate expression suggest possible species in these systems.
+
Introduction I n a previous publication,Z we pointed out that welldefined, separate nmr peaks are observed for HzO and XHa protons at room temperature in HzO-NH~solutions containing roughly 30 mol % or less HzO. Thus the exchange of protons between HzO and XH3 is slow in the nmr sense under these conditions. We further demonstrated that this exchange could be markedly accelerated by addition of NH4+, and we reported on the results of a study of the kinetics of Hz0-NH3 proton exchange accelerated by N H 4 f . I n this paper we report results of a study of H20-NHa proton exchange accelerated by hydroxide. This process is slower than the process involving KH4+ and is dependent on HzO concentration in a way that suggests more than one HzO species in the Hz0-NH3 liquid system a t room temperature. Moreover, under certain experimental conditions, the NH4+ arising from the ionization of HzO can be detected and rather narrow limits can be placed on the ionization constant for H2O at certain concentrations in liquid KH3.
Experimental Section Proton line width data were obtained using the Varian DA-60 instrument. All measurements were
+
made at the equilibrium temperature in the nmr probe which was found to be very stable at 29.6 =t0.2’. A given Hz0-NH3-KOH solution was prepared by mixing a measured amount of an appropriate dilute aqueous KOH solution with a measured quantity of anhydrous liquid KH3. The samples were prepared and examined in the special plastic-valve, glass nmr cell shown in Figure 1. Because of its small size, light weight, and axial symmetry, the cell can be spun and a resolution of 0.3 Hz at 60 MHz can be obtained. The glass section is standard 1-mm wall X 5-mm 0.d. Pyrex glass tubing, selected from several lengths of commercial stock for roundness and precise 0.d. A slightly enlarged section near the open end of the glass tube permits firm attachment of a plastic valve. The stem-inlet of this valve is machined to the standard-taper angle to fit a ground joint on a glass vacuum system. The stem was removed completely for introduction of the aqueous KOH solution with a calibrated micropipet. The reassembled cell was then placed on a vacuum system, and the glass tube was cooled in liquid and evacuated. NH3 was then added from a calibrated volume filled to a (1) Work done under the auspices of the U. S. Atomic Energy Commission. (2) M . Alei and A. E. Florin, J. P h y s . Chem., 72, 550 (1968).
Volume 7% Number 4 April 2069
