S T E R E O C H E M I S T R Y OF O R G A N O P H O S P H O R U S C O M P O U N D S

V. MO LCAO CALCULATION OF SPIN-SPIN INTERACTION CONSTANTS IN

(CH3)3PO, (CH3)2P(O)Ot-I, CH3P(O)C12, H3PO 4, CH3PH z, AND (Ct-t3)3P MOLECULES

R. K. S a f i u l l i n , R. M. A m i n o v a , UDC and Yu. Yu. S a m i t o v

539.194 + 541.63 + 541.67

In the formalism of Pople and Sanity an MO LCAO calculation was made of spin-spin interaction constants of nuclei in (CH 3)3pO, (CH3) 2P(O)OH, CH3P (O)C12, H~PO4, (CH 3)uP, and CH3PH 2 molecules. The relations of the constants ~IHPCH, 3hToPCH and 3hvOPOH to the dihedral angles were found, and also the stereospecificity of the constants llI3CH and 2131PCH was examined. The numerical values of many of the constants and their angular correlations agree fairly well with the experimental data. The worst agreement is found for the constants llt3cH which are about 60% of lh3cH expt. The influ- ence of the orientation of the unshared electron pair of the phosphorus atom in methylphosphine on the value of the constant 3IHPCH is pointed out. A discussion is given of the possibility of the appli- cation of the relations calculated for conformational analysis and in the stereochemistry of organo- phosphorus compounds.

The exceptional importance of the stereospecifictty of proton-proton geminal, vicinal, and long-range spin -sp in interaction constants (coupling constants) for conformational analysis and the stereochemistry of organic compounds as a whole is well known. In flue experimental study of the steric structure of molecules and the dy- namic stereochemistry of organophosphoms compounds by methods of 1H and 31p NMR spectroscopy the values of the coupling constants of magnetic nuclei with the alp nucleus acquire no less importance. Up to now several suc- cessful attempts have been made to establish the stereospecificity of the vicinal coupling constants 3131POCH [1] and 3131PCCH [2-4] on the basis of empirical data. However, many questions in this field still remain little stud- ied and poorly understood. By carrying out the present work we hoped to obtain supplementary information on some angular correlations of coupling constants for interaction with the 3lp nucleus.

Coupling constants were calculated taking account of only contact interaction in the approximation of Pople and Sanity [5]. We examined the molecules CHaP (O)C1 z (I), (CHa)3P0 (II), (CH3)zP(O)OH (III), HH3PO 4, CH3PH 2 (IV), and (CH3)3P (V). Taking account of only one-center integrals for the s orbitals of the interacting atoms, we may present the starting formula for the constant IAB e~ in the form

- a B = hy.~TB <q~a 15 (r.)l w~> <w~ 16 (rB)l wB> I I~B,

oee vac IIAB = 4 ~ ~ (e~ - - ~)-~ C~AC~BCiaCjB,

i j

in which < ~AI 6 (rA)] r > is the density of the valence s electron of the atom A on the nucleus, and ei and ~. are one-electron energies corresponding to the molecular orbitals ~i and ~Oj, which are constructed in the form of LCAO:

V. I .Ul 'yanov--LeninKazan' State University. Translated from Zhumal Strukturnoi Khimii, Vol. 16, No. 1, pp. 42-48, Ianuary-Febmary, 1975. Original article submitted May 15, 1973.

�9 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part o f this publication may be repro- duced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, micro- filming, recording or otherwise, without written permission o f the publisher. A copy o f this artMe is available from the publisher for $15.00.

36

Ol0 30 60 ,90 ,~,:.'O 1/.,0 Z,~O ~

\ . . i - - + ,= i [! \ ~+

\

+'i -2

-3

~d Hz JTOPGH'

7 \

7 ~ .

i ' P I" + I . + " ~ i + +o 20 +';+a+o--1++ +co+

Fig. 1. Calcula ted angular dependence of the

geminal constant ~IatPCH in the molecules CHaP (O)CI~ (I), ( CHa)aPO (II), and (CH3)2P(O)OH (III).

Fig. 2. Calcula ted angular dependence of the

vic inal constant ahTO= PCH in the molecules CHAP( O)C12 (I), (CHa)aPO (IlL and (CHa)2P(O)OH (III).

.L Hz Jr

/;,'0/'5~ ;du 0

-21

Fig. 3. Calcula ted angular dependence

of the v ic ina l constant 31170 = POH in the molecu le HaPO 4.

As basal a tomic orbitals we used Slater functions with exponents ob-

tained in SCF calculat ions [6]. The exponent for the 3d orbttals of the

phosphorus atom was taken to be 1.00. Values of s i and Cig were de- termined by solving the secular equation

IH.,~--s$,+ I = O

on an M-220 e lect ronic computer by the program given in [q] supple-

mented by us by a block for the calcula t ion of gAB- The matrix e l e - ments of the Hamil tonian were ca lcula ted from the Wolfsberg-Helmhol tz

formulas [8]:

IJ-,~tu. ~ - -~ . .~

The ionizat ion potentials Ig for the corresponding valence states of the atoms in the molecules were chosen in ac- cordance with [9]. For 3d orbitals of the phosphorus atom i t was assumed that I ~ = 1.90 eV. The geometr ic param- eters of the molecules were taken by us from [10-12]. The va lence angle < POH in the molecules (CHa)2P(O)OH

and HaPO 4 was taken to be 118 ~

C o u p l i n g C o n s t a n t s in P h o s p h o r u s ( V ) C o m p o u n d s

Below we give the results obtained in an examinat ion of the compounds (I)-(III) with a 4-coordinate phospho- rus atom. On the basis of these we may trace the relat ion of the gemina l constant aI31PCH to the dihedral angle 0 between the planes of C - P = O and P - C - H and also to the s character of the P - C bond. Figure 1 gives graphs

of 2131 PCH = f (O) for the compounds ( I ) - ( I I I ) . It is known [18] that the rep lacement of substituents on the central a tom by more e lec t ronegat ive substituents leads to the concentration of s character in the direction of other bonds of the central atom, which must intensify contact sp in - sp in interaction. The results obtained are in accord

with this view. Thus, by averaging over the orientations we obtain for compounds (I), (II), and (III) the values of

2131PCH = - 19.1, - 1 4 . 0 and - 1 7 . 4 Hz, respectively. For (I) a notable feature is the except ional ly strong depend- ence of J31pc H on the orientation, whereas for (II) and (III) the curves are ex t remely similar and no strong depend- ence is observed. As regards the numer ica l values of the constants and their signs, the ca lcula ted quantit ies are, in

our opinion, in good agreement with the exper imental values of 2J31PCH, which for compounds with a 4-coordinate phosphorus a tom usually l ie in the range from - 1 8 t o - 2 0 g z [14].

For ( I ) - ( I I I ) we also ca lcu la ted the relat ion of the v ic ina l constant 3h70= PCH to the dihedral angle O. These angular correlations are shown in Fig. 2, and it can be seen that for(II) and (Il l) the curves are again s imi- lar in character, and the value of the constant varies within the l imits i 3 Hz. In all three cases the change in the sign of the constant occurs at O ~ 105 ~

37

~]~'pc, Hz :15 f

I0 / ' / i/D 5

/ /

o , _2_, ' . ,o 0 BO bO O0 i?y ,@i; s80O

i _~I.

,0L /

3 Jttl;P fl ' HZ iO

5

0 so e ' t5o 18o o

Fig. 4. Calculated angular dependence of the geminal constant zJ31PCH in the molecules CHaPH z (IV) and (CHs)aP (V).

Fig. 5. Calculated angular dependence of the vicinal constant 3JHPCH in the methylphosphine molecule.

~,3C_H, HZ 80

80.

.. ". ,,'

74

b -j .'~ "./ " ' - _ _ 1 %

,oi..;/ o so 6'0 3o

Fig. 6, Calculated angular dependence of the direct constant iJ13 C in the mole - cules CHstKO)C12 (I), (CHs)aPO (II), (CH3)2P(O)OH (III), CHsPH z (IV), and (CHa)aP (V),

Figure 8 shows the calculated relation of the vicinal constant ShTo= POH in the H3PO 4 molecule to the dihedral angle between the planes of O = P - O and P - O - H , which isreminiscent of the graph given above for 3J170= PCH. Unfortunately, there are no data in the literature at present on the numerical values of stereospecificity of

31170= PCH and 3h70= POH constants.

C o u p l i n g C o n s t a n t s i n P h o s p h o r u s ( I I I ) C o m p o u n d s

a) The stereospecifieity of the gerninal constant zJstPCH has been discussed previously on the basis of purely empir ical data. For exam- pie, Albrand and co-workers [15] showed that the value of 2JalPCH in phosphines is determined by the relative disposition of the plane of the P - C - H fragment and the plane of C - P - ( U P ) (UP = unshared pair of phosphorus atom). At present it is not clear whether Albrand's empir i - cal angular correlation can c la im generality, since it is constructed with the use of experimental values of ZIslpCH for compounds in which the endocyclic phosphorus atom has eonsiderably differing angular strains, while the geometric parameters were not determined with sufficient ac- curacy. Also, the value of the constant 2J31pc H, equal t o - 0 . 0 g Hz for triethylphosphine, does not correspond to Albrand's curve. We calcu- lated the angular dependence of the constant zlalPCH for the aliphatic

phosphines (IV) and (V). The dihedral angle 0 was reckoned from the ( U P ) - P - C plane to the P - C - H plane. The relations obtained are shown graphically in Fig. 4. From them it can be seen that the constant zJslpc H changes sign from negative to positive at 0 ~ 125 ~ whereas on Albrand's graph the change of sign frcrn positive to negative oc- curs at 0 ,,, 80 ~ According to the experimental data [16], in the molecules of (V) and (IV) the constants zJ31pctt are + 2.66 and + 8.99 Hz, respectively. As the most stable conformations for these molecules we may present the following triply degenerate rotameters:

H ~ / ~ / I : I I I - _r~ H

]l ( CH a tt [ ]t 1(

Then, from the graph of Albrand and co-workers we can find the following expected value of the constant:

:~J:,,PCH ~ ;'-~- ! [ 2 2 j g a u c h e + t '~jtrans] : - + 3,3 Hz,

while according to our data the expected value of the constant is ZlsiPCH ~ - 3.6 Hz. Thus, both results lead to

38

o

0

0

u

r ~

N

+ I

c o

-b i -b t

~o

-F [ i I

t ~ 0

o

J

~o o~ o 0 ~

+ § I $ o o

~.o " ~ c~ ~

I + ~ I H- / I aO ~ ~ o ~, o o 6 o

I -F

ke~

t ~ J

o o L~

I

+ + # + t o o ~ o o

5 I

c~ ~ o I o

SS

I t E, ~ I ~ IJ ] I ~ ~ 0 ~ ~ I 0 0 0

39

similar absolute values of the constant llalPCH, but the sign of the constant obtained from our graph is the opposite from that given in [16].

b) The stereospecificity of the vicinal constant alHPCH has scarcely been discussed in the literature, but for the study of the stereochemistry of phosphines it may play an important role. Figure 5 shows the calculated rela- tion of aJHPCH in the methylphosphine molecule to the dihedral angle between the H - P - - C and P - - C - H planes. In character this relation is reminiscent of the curve of Karplus for the constant ~IHCCH, but, as the graph shows, it leads to a somewhat low value of the averaged constant aIHPCH in methylphosphine, which is+ %88 Hz [16]. In Fig. 5 there are two graphs. The upper one corresponds to the case in which the dihedral angle between the (UP) - P - C and P - C - H planes approaches 90 ~ while the lower curve corresponds to the case in which this angle is close to zero or 180 ~ We must point out that an exactly similar situation was observed by us earlier for the CHaNH~ molecule. We must also mention that for the relation given above for the constant zJalpc H in the (CHa)2P(O)OH mol- ecule ambiguity is again found. Here the maximum difference in the constant for angles of identical magnitude but reckoned in opposite directions was 1.8 Hz. For the other relations given above the deviation did not exceed 0.5 Hz. It proved difficult to obtain more detailed information for these molecules.

S t e r e o s p e c i f i c i t y o f t h e D i r e c t C o n s t a n t l I l a C H

The spin-spin interaction between directly linked nuclei of the laC carbon isotope and hydrogen, observed in PMR spectra as satellite signals and observed directly in iac NMR spectra, can also serve as means of studying the mutual spatial disposition of groups of atoms in molecules of organic compounds. Unfortunately, there is very little information yet in the literature on the influence of the steric disposition of atoms in a molecule on the constant iJlaCH. This is largely determined by the fact that every method of reeording lac NMR spectra is usually conducted under conditions of monochromatic or noise spin decoupling (total heteronuclear double l aC-{ IH} NMR), in which any I13CH constants are effectively "averaged" to zero. There can be no doubt that in the future the stereospeci- ficity of the "direct" constant lIlaCH will be applied for the solution of stereochemical problems, including the stereochemistry of organophosphoms compounds. We shall therefore also examine this coupling constant.

The calculated curves for the relations of the direct constant ihsCH to the dihedral angles are given in Fig. 6. For molecules with 4-coordinate phosphorus the angle between the O = P - C and P - C - H planes is plotted as ab- scissa, and for molecules with a-coordinate phosphorus the angle between the ( U P ) - P - C and P - C - H planes is plot- ted as abscissa. The calculated values of the constant iJlaCH are ~ 60% of the experimental values, equal to about 120 Hz (128.0 Hz in methylphosphine). As was established theoretically in [1~, 18], the direct constants IJXH are related by a cubic equation to the charge on the atom X. Hence, such low values of the constants, characteristic for this approximation, may be explained by the inaccurate determination of the charges on the atoms that is char- aeteristic for the Hoffman method [19]. We should mention that the CNDO method, for example, which gives bet- ter values of the charges on the atoms, enables us to obtain direct constants *JIaCH that are close to the experimen- tal values. For these relations of the constants lhaCH ambiguity was again observed, and the greatest deviation ( ~ 6 Hz) was obtained for the molecule of(II) . From the graphs it can be seen that the direct constant 1linCH is particularly sensitive to details of the electronic structure of the molecules, and it therefore should be used for the investigation of their steric structure with great caution.

C O N C L U S I O N S

The further application of this approximation to the examination of other coupling constants shows that the numerical values of, e.g., the geminal constants zIHC H in the molecules of (I)-(V) are in good agreement with the experimental data. In this case also, an extremely strong influence of the steric disposition of the interacting pro- tons relative to adjacent groups of atoms is observed. The limits of the changes in the constants 2IHC H and the contact contributions in the other constants are given in Table 1.

In conclusion, we can maintain that, despite the crude character of the approximation contained in the for- realism used, it leads to fairly good values of the coupling constants: low for direct and vicinal coupling constants, but quite reasonable for geminal coupling constants, when it is even superior to CNDO and INDO methods~ This can be explained on the view that, although in this method the interaction of electrons with one another is not taken in-

to account explicitly, the actual evaluation of the matrix elements of the HamNtonian involves in some degree an implicit allowance for this interaction. It may be hoped that the angular relations discussed will be of definite in- terest for conformational investigations by the NMR method and for stereochemieal investigations of organophospho- ms compounds. To improve the accuracy of the results it is necessary to perform calculations with the use of other semiempirical methods. Our future publications wiI1 be devoted to these questions.

40

L I T E R A T U R E C I T E D

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of the USSR, Kazan' (1972). 12. H.R. Linton and E. R. Nixon, Speetrochim. Acta, 15, 146 (1989). 18. H.A. Bent, I. Inorg. Nucl. Chem., 19, 43 (1961). 14. B.I. Ionin and T. N. Timofeeva, Usp. Khim., 41, 758 (1972). 1S. I .P . Albrand, D. Gagnaire, I. Martin, and I. B, Robert, Bull. Soc. Chim. France, 1969, 40. 16. S.L. Manatt, G. L. Iuvinall, R. I. Wagner, and D. D. Ellman, I. Amer. Chem. Soc., 8-8, 2689 (1966). 17. D.M. Grant and W. M. Litchman, J. Amer. Chem. Sot., 8_7.7, 8994 (1965). 18. L N. Shoolery, I. Chem. Phys., 3-1, 1427 (1959). 19. tL Hoffman, I. Chem. Phys., 89, 1397 (1963).

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