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eliminated by a simple iterative process prescribedby jlcWeelly9.

Applicability of the method - Although a steepestdescent procedure guarantee" convergence, veryoften the convergence is rather poor. It is thusnecessary to test whether a particular methodinvolving a steepest descent procedure leads toreasonable convergence to be of any prLlctical value.For this we have done two test calculations theresults of which seem quite encouraging.

In Table 1 we present the electron densities onthe terminal atoms of allyl cation after successiveiterations using the present method. The resultsobtained by the conventional o-technique" andthose improved by Hakala's method" are alsoincluded in Table 1. A comparison among thethree sets shows a great improvement in the con-vergence by the present method.

Conventional w-teclll1ique is known to lead toa divergence for benzyl cat ioi.s. Convergence canonly be achieved by the application of ratherelaborate methods involving averaging after succes-sive iterations? or including w'- and {o"-techniqueslo.In Table 2 we present the electron densities onthe first atom (outside the ring) of benzyl cationafter successive iterations using the present method.A comparison with the values given in lit erntnretagain shows a great improvement in the convergenceby the present method.

In order to see whether the charge densitiescalculated by the present method give a betterpicture of the actual -e-electron charge densitiesthe authors have started calculations of dipolemoments of a series of non-alternants using thecharge densities obtained by the present method.The results of those calculations, which will bepresented in a later paper, are expected to be veryhopeful indeed. The values of dipole momentsof fulvene and azu lcn« so far calculated appeareven better than those10 obtained by (0'- and w"-

TABLE 1 - ELECTRON DENSITIES ON THE TERMINALCENTRES OF ALLYL CATION AFTER SUCCESSIVE ITERATIONS

No. of Present As in As initerations method ref. 3 ref. 8

0 0·500 0·500 0·5001 0·601 0·621 0·6212 0·598 0·534 0·5793 0·598 0·597 0·569

10 0·571

TABLE 2 - CHARGE DENSITIES ON THE FIRST ATOM (i.e.THAT OUTSIDE THE RING) OF BENZYL CATION AFTER

SUCCESSIVE ITERATIONS

No. of Present cu- Technique' Arithmeticiterations method mean'

0 0·5714 0·5714 0·57141 0·3680 0·1697 0·37012 0·3510 0·5697 0·39383 0·3182 0·1532 0·37264 0·3158 0·5879 0·39485 0·3140 0·1212 0·3728

techniques. In conclusion we may say that as theconvergence here is quite good, the charge distri-butions and hence the dipole moments are betterthan those obtained by the conventional w-tecitniqueand as the method avoids repeated diagonalizationof the Hamiltonian matrix, generally a timc-cor.si.m-ing step in a self-consisted field calculation, thepresent method seems to have a significant promiseand hence should be extensively appliEd.

One ofthc authors (N.G.lVI.)is indebted to Prof. R.McWceny of the University of Sheffield, UK, formaking him acquainted with the principles of thesteepest descent technique ar.d to the UGC, NewDelhi, for financial assistance. The authors arcalso grateful tc the Centre of Computer Science,University of Calcutta, for computer facility.

References

1. COULSON, C. A. & RUSHBROOKE, G. S., Proc. CambridgePhil Soc., 36 (1940), 193.

2. MCVVEENY, R., Molecular orbitals in chemistry, physicsand biology, a tribute to R. S. Mulliken, edited byP. O. Lowdin & B. Pullman (Academic Press, NewYork), 1964, 304.

3. STREITWIESER, (Jr) A., Molecular orbital theory fororganic chemists (John Wiley, New York), 1961.

4. HARRIS, F. E., J. chem, Phys., 48 (1968), 4027.5. GOODISMAN, J., Theoret. Chim. Acta (Bern, 36 (1974),

117.6. STREITWIESER (Jr), A. & NAIR, P. M., Tetrahedron, 5

(1959), 149.7. COULSON, C. A. & VVILLE, F., Tetrahedron, 22 (1966),

3549.8. HAKALA, R. W., Intern. J. Quantum Chem. (Symposium),

1 (1967), 227.9. MCWEENY, R., Proc. ray. Soc., A235 (1957), 496.

10. STREITWIESER (Jr), A., HELLER, A. & FELDMAN, M., J.phys. Chem., 68 (1964), 1224.

Floating Spherical Gaussian Orbital (FSGO)Studies with a Model Potential: Methane,

Silane & Germane

S. P. MEHANDRU & N. K. RAY*

Department of Chemistry, University of Delhi, Delhi 110007

Received 30 December 1976

A Gaussian-based model potential is used withinFSGO formalism to study the equilibrium geometriesof CH.. SiH. and GeH.. The predicted bond lengthsare in excellent agreement with the experimental values.

VALENCE electron studies with model potentialshave drawn considerable attention in recent

years1-IS• Most of these calculations have beenmade within the LCAO-SCF-MO formalism andonly a few have been carried out in the frameworkof floating orbital basis4,5,10,16-IS.

In the present communication we have used themodel potential suggested by Schwartz andSwitalski-" within FSGO formalisms? to study theequilibrium geometries of CH4, SiH4 and GeH4•

This method has been used quite successfully earlierby Ray and Switalski to study the first row atom

. *Author to whom all correspondence should be made.

145

INDIAN J. CHEM., VOL. 15A, FE~RUARY 1977

hydrides'" and a series of two-valence electron di-atomic and triatomic ions", The core model poten-tial used here has the form

V m = _ Zc +[A. or AI'] exp (- yr2) ... (1)r r

where Zc is the nuclear charge minus the numberof core electrons. As and AI' are the model poten-tial parameters for the sand p state of the atomunder consideration. Core model potential para-meters needed for the present study arc obtainedby a procedure similar to the one suggested earlierby Ray and Switalski17,18. These parameters arelisted in Table 1.

Only valence electrons are taken into considerationand the effect of the core is simulated through theuse of a model potential. The molecular wavefunction is constructed using the FSGO method-".The floating basis orbital does not possess a weIl-defined angular momentnm-t. Because of thisarbitrariness in the components of the angularmomenta of the FSGOs, Vm as defined in Eq. (1)cannot be directly used. An effective A (Aav) shouldbe used which should be a function of As and AI"The Aav values are listed in Table 1 and are obtainedusing Eq. (2).

A = k [AsN.+ApNp ]av N.+Np •.• (2)

where Nand Np are the number of sand p valenceelectrons respectively. k is a constant equal to 1 forfirst row atoms and is 0·75 for the second and thirdrow atoms. Hence, the model potential used inthe present study reduces to the form

V":=_~C+Aav[eXP ~_Yr2)] ... (3)

The best values for the positions of the Gaussians,orbital radii and the nuclear positions are obtainedby minimizing the valence energy, Eval. Theoptimization is carried out using the subroutineSTEPlp2. Tetrahedral geometry (Td) was main-tained for all the molecules studied here during theoptimization.

The results of the present study are given inTable 2. The predicted bond lengths are in excellent

TABLE 1- MODEL POTENTIAL PARAMETERS FOR C, Si AND Ge

Atom As Ap Y Aav

CSiGe

2·67652·89782·7510

1·0820·47100·4156

1·25181·68941·6301

-0·17291'60721·5959

TABLE 2 - RESULTS FOR THE BOND LENGTH OFCH4, SiH4, GeH.

Molecule Bond length (a.u.)

Modelpotential

FSGOa Exptl»

2·142·762·82

(a) Obtained from references 25 and 26.(b) Obtained from references 27 and 28.

2·112·80

2·102'762·89

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TABLE 3 - CALCULATED AVERAGE POLARIZABILITIES(UNITS OF 10-25 CM")

Molecule Average polarizabilitye

Modelpotential

FSGO

29·658·558·7

24·444·0

(a) Average polarizabilities were calculated using theprocedure given by Amos and Yoffe in reference 23.

agreement with the experimental values andthe results of the other ab initio studies25,26.

Recently Amos and Yoffe23 have used symmetryadopted perturbation theory24 to successfully cal-culate the average electric polatizabilities of mole-cules from FSGO wave functions. In view of thisfact it was considered worth while to compare ourcalculated polarizabilities with those obtained fromnormal FSGO studies. Our calculated results aregiVl'1l in Table 3 along with those obtained fromFSGO wave functions. Fairly good agreementbetween the two is observed. The model potentialmethod used here appears to be quite promising.We are currently extending the method for the studyof larger polyatomic molecules. These results willbe reported elsewhere.

A part of the work presented here was carriedout at the University of North Carolina at ChapelHill, USA. One of the authors (N.lK.R.) thanksProf. Robert G. Parr for his warm and r,eneroushospitality at Chapel Hill. Thanks are also dueto Dr J. D. Switalski for helpful discussions.

References1. KUTZELNIGG, W., KOCH, R. J. & BINGEL, W. A., cue«:

Phys. LeU., 2 (1968), 197.2. SIMONS, G., Chem, Phys, Lett., 18 (1973), 315.3. SIMONS, G., J. chem, Phys., 55 (1971), 756.4. BARTHELAT, J. C. & DURAND, PH., Chem. Phys. Lett.,

16 (1972), 63.5. BARTHELAT, J. C. & DURAND, PH., J. chim. Phys., 71

(1974), 505, 1105.6. KLEINER, M. & MCWEENY, R., Chem, Phys. LeU., 19

(1973), 479.7. MELIUS, C. F., OLAFSON, B. D. & GODDARD, W. A. III,

Chem, Phys. LeU., 28 (1974), 457.8. POHL, H. A. & FOWLER, D. R., Intern. J. Quantum Chem.,

8 (1974), 435.9. MELIUS, C. F. & GODDARD, W. A. III, Phys. Rev., 10

(1974), 1528.10. GASPAR, R. & TOMASSy-LENTEI, 1., Acta Phys. Acad.

Sci. Hung., 33 (1973), 387.11. SWITALSKI, J. D., HUANG, J. T. H. & SCHWARTZ, M. E.,

J. chem. Phys., 60 (1974), 2252.12. SWITALSKI, J. D. & SCHWARTZ, M. E., J. chem, Phys.,

62 (1975), 1521.13. ZERNER, M. C., Mol. Phys., 23 (1972), 963.14. HORN, M. & MURRELL, J. N., J. chem, Soc., Faraday II,

(1974), 769.15. MURRELL, J. N. & VINCENT, 1. G., J. chem, Soc., Faraday

II, (1975), 890.16. SEMKOW, A. M., SUTHERS, R. A. & LINNETT, J. W.,

Chem. Phys. Lett., 32 (1975), 116.17. RAY, N. K. & SWITALSKI, J. D., J. chem. Phys., 63

(1975), 5053.18. RAY, N. K. & SWITALSKI, J. D., Theoret. cu«. Acta,

41 (1976), 329.

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19. SCHWARTZ, M. E. & SWITALSKI, J. D., J. chem, Phys.,57 (1972), 4125.

20. FROST, A. A., J. chem, Phys., 47 (1967), 3707.21. CHRISTOFFERSEN, R. E., SPANGLER, D., HALL, G. G. &

MAGGIORA, G. M., J. Am. chem. Soc., 95 (1973), 8526.22. Obtained from QCPE, Chemistry Department, Indiana

University, Bloomington, Indiana 47401, USA.23. AMOS, A. T. & YOFFE, J. A., Chem, Phys. LeU., 31

(1975), 57.24. AMOS, A. T. & YOFFE, J. A., cu«. Phys. Lett., 31

(1975), 53.25. CHU, S. Y. & FROST, A. A., J. chem. Phys., 54 (1971), 760.26. FROST, A. A. & ROUSE, R. A., J. Am. chem, Soc., 90

(1968), 1965.27. PAULING, L., The nature of the chemical bond (Cornell

University Press), 1960.28. MOCCIA, R., J. chem, Phys., 40 (1964), 2164, 2176, 2186.

Strong SolventChemical Shift

Dependence ofin Lanthanide[(CH3);!PSJ3Ln

PhosphorusComplexes

G. HAGELE, W. KUCHEN & P. N. MOHAN DAS

Institut fur Anorganische und StrukturchemieUniversitat Dusseldorf, Universitatsstrasse 1

4000 Diisseldorf, 'West Germany

Received 13 December 1976; accepted 27 December 1976

The IH and IH(31P) NMR spectra of the paramag-netic complexes LnL3 [Ln= Pr(III), Nd(III), Eu(III),L=(CH3)2PS2] are found to be strongly solvent de-pendent. Solutions in acetone-d. exhibit greater haH-widths in P-CH3 doublet and larger lip values than thecorresponding solutions in methanol-d •.

REACTIONS between stoichiometric amountsof lanthanide ions and the sodium salt of

dimethyldithiophosphinic acid (CH,')2P(S)SNa.2Hpin ethanol medium gave the octahedral complexesof the type (1)1.

[(CH3).P /S'\...]3L-l

"'s/I

Ln=La(III), Pr(III), Nd(III), Eu(III), Sm(III)

2LHz

TMS TMS TMS

A 8 c

Fig. 1 - 60 MHz NMR spectrum for protons in[(CH3),PS')]3Pr [40 mg complex dissolved in 0·4 ml of solvents:CD,COCD. = A; CD3COCD,/CD30D (1: 1) = B; and

CD30D=C]

It is found that the 60 MHz IH and IH(31P) NMRspectra of the paramagnetic Pr(III), Nd(III) andEu(III) complexes are strongly solvent dependent.Solutions of I in acetone-a, exhibited greaterhalf-widths in P-CH3 doublet lines and larger ap

values than in methanol-a, (see Fig. 1). An unusualstrong sensitivity of ap in I towards change of thesolvent is observed. ap values were observed inthe wide range of about 100 ppm widths (see Table1). As we were able to prepare well-defined di-adducts, LnL3.2B of some complexes (I) (e.g. Ln=Pr(III); L= (CHa)2PS2; B=CHaOH, CsHsN) asstable solid compounds, we assume that thecoordination number six in I is expanded to eightin the solutions of the above-mentioned solvents.We suggest that the magnitude of the extremelystrong shift in ap and the change in the spectralhalf-widths may be in correlation with the solventdonor properties. Therefore, we intend to usethe paramagnetic complexes (I) in particular[(CH3hPS213Pr for systematic studies of their inter-actions with a wide variety of donor solvents.

References

1. MOHAN DAS, P. N., KUCHEN, W., KECK, H. & HAGELE, G.,J. inorg. nuci. Chem., (in press).

TABLE I-SOLVENT DEPENDENT CHEMICAL SHIFTS OF PHOSPHORUS, PROTON AND SPECTRAL HALF-WIDTHS OF P-CH3 DOUBLETS

Compound CD3COCD, CD,OD

OP oIl tJ.vl/2 op OH tJ.vlj2

LH 2-117 0·5 +50·9 2'083 0·5LaL3 +52·2 2·000 1PrL3 +19·2 1-167 10 -51-4 -0·242 3NdL3 -26,7 2·767 15 -58,4 1·558 1SmL3 +57·6 1·783 10 +53·7 1·792 6EuL3 +51·2 -0·222 3·5 -24,3 1·735 1·5

oP= phosphorus chemical shift calc. vs H.PO. 85% (ppm).OH= proton chemical shift vs TMS (ppm).tJ.vI/2 = spectral half-width of P-CH3 doublets (Hz).LH = (CH,hPS2H.

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