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American Mineralogist, Volume 58,pages 75G764, 1973

Etfectof Variationsin O-P-Oand P-O-PAngleson P-O Bond OverlapPopulations for SomeSelectedOrtho-and Pyrophosphates GroncB A. Lecen.l eNn G. V. Grsss Department of GeologicalSciences Virginia PolytechnicInstitute and State Uniuersity Blacksburg, Virginia 2406I Abstract Extended Hiickel molecular orbital (ruivro) calculations for hypothetically distorted PO.& and PrO"- ions predict that shorter P-O bonds on the average should be involved with wider P-O-P and O-P-O angles. Plots of P-O bond length us the average of the three O-P-O angles common to each bond, and of (P-O(br)) us P-O-P angle, confirm this for selected ortho- and pyrophosphates. Bond overlap populations, n[P-O], calculated with all P-O bond lengths clamped at 1.50 A, tend to be larger for shorter observed P-O bond lengths. The P-O bond lengths in herderite, CaBePOr(OH), are estimated from sulvro theory using a relation betweenbond overlap population and bond length. As f(O), ntP-Ol, bond number and o-bond order are highly correlated, caution should be exercised in making inferences about the nature of a bond because any one of these parameters appears capable of providing a plausible interpretation of bond length and angle variations. It appears that both f(O) and n[P-O] measure a similar property of the P-O bond.

Introduction

examinationof the Pauling-Cruickshankd-p o'bonding model,Bartell, Su, and Yow (1970) havefound that Mulliken bond overlap populations, n[P-O], calculatedfor a number of phosphatescorrelatewith the simpleo-bond ordersworked out by Cruickshank (1961). They observedgood correlation between P-O bond length and nlP-Ol even though all P-O distanceswere held constantat 1.50 A during the calculations. They also conclude that all five 3dorbitals participate in bonding instead of just the two asproposedby Cruickshank( 1961). The presentstudy (Lager, 1972;Lager and Gibbs, 1972) was undertakento evaluatethe effect of the variations in the O-P-O and P-O-P angles on ntP-Ol and P-O bond length, relationshipsnot consideredby Bartell et al (1970). Evidencewill be presentedwhich will show that r[P-O] values are strongly dependent upon angular variations indicating that shorter P-O bonds on the averageshould be involved in wider O-P-O and P-O-P angles.In addition, the similaritiesbetween bonding models will be discussed. andparameters

In 1939,Pauling proposedthat phosphorusmay utilize its outer 3d-orbitalsin a double-bondformation with its coordinating oxygen atoms becauseit is not rigorously restrictedby the octet rule. Expanding upon this proposal, Cruickshank (1961) has assertedfrom group-theoryargumentsand approximate molecular orbital calculations that only two of the five 3d-orbitals,3d,,-o" and 3d",, are actually used in double-bond formation in POn tetrahedra. Employing a model for establishingbond strengths, he worked out the r-bond orders for the tetrahedral bonds in a number of phosphatesand found that they correlate well with the observed P-O bond lengths. Cruickshankpredicted from his model that: (l) P*O(nbr) bonds should be shorter than P-O(br) bonds and (2) the length of the P-O(br) bond should increaseas the P-O-P angle decreases.Brown and Gibbs' (1970)scatterdiagramsof (P-O(br)) and of t€-O(br))-(P-O(nbr))l versus P-O-P angle apparently substantiate both predictions. Recently Baur (1970) demonstratedthat the steric details in phosphatescan also be rationalized in terms of his CorrelationsBetweenBond Overlap Population and extendedelectrostaticmodel. P-O Bond Length In an extendedHi.ickelmolecularorbital (pnuo) The phosphatesselectedin our study are given in l Now at the Department of Geology, University of British Table 1 together with their calculated Mulliken Columbia, Vancouver 8, British Columbia, Canada. (1955) bond overlappopulations,n[P-O], and ob756

VARIATIONS

IN O-P4

TesI.e l. Observed bond lengths and calculated bond overlap populations for selectedphosphates.

ANGLES

P-OGr)

P-o(nbr)

P-o-l.50

757

T^c.sre 2. Valence orbital ionization potentials (von) and orbital exponents(f). Aton

(p+ll Bond

AND P4_P

Atonic

Orbiral

Oxygen

2e 2p

-35.13 -13.62

2.275 2.275

Phosphorus

3e 39 3d

-20.30 -tl,00 -2.50

1.600 1.600 1.100

(ca1vo, 1967) s-Me2P 2o7 P(1){(1) P(1)-o(2) P(1){(3) P(1)-o(4) P(2)-o(r) P(2)-o(s) P(2){(6) P(2)-o(7)

1.613

1.568 1.535 L.526 L.52L d-calp

P(1)-O(1) P(r)-o(2) P(1)-o(3) P(1)-0(4) P(2)-o(1) P(2)-o(5) P(2)-o(6) P(2)-0(7)

2o7

(Celvo,

.625 .648 ,587 .599 .530

1968)

r.s79 1.518 r.52r. 1.507 1.616 1.s35 r.508 |.493 8-cs"P"o.

P(l)-o(r) P(1)-0(2) P(1)-o(3) P(r)-o(A) ?(2)-0(r) P(2)-o(5) P(2)-o(6) P(2)-o(7) P(3)-o(8) P(3)-o(9) P(3)4(10) P(3)-O(rr) P(4)-o(8) P(4)-o(12) P(4)-O(13) P(4)-o(14)

0.620 .642 .641 ,654 ,624 .647 .617 .648

1,535 r,505 L.473

0.62L .550 .54r .637 .618 .648 ,642 .642

0.587 .645 .634 .643

.662

(Uebb, 1966)

1.637 r,50s 1.538 1.519 1.61s 1.480 1.530 r,526 1,589 1.498 1.504 1.563 1,518 1.s03 r.527 !.s27

0,610 .638 .647 .653 ,610 .644 .645 .650 .62r .649 ,647 ,639 .61r .539 .651 .651

0.541 .654 .632 .655

.633 .64r

.602 .654 .644

d-Cu2P207 (Robertson and Ca1vo, 1967) P(1){(1) P(1)-o(2) P(1)-o(3) P(1)-0(4) P(2)-o(1) P(2)-o(s) P(2)4(5) P(2)-o(7)

1.578 1.s33 L-478 1.517 r.s80 I.545 r.562 1.518

0.639 .632 .64L .649 .625 ,642 .640 .653

VOIP(ev)

0.s97 .515 ,66s .644 ,594 ,824 ,509 .657

servedP-O bond lengths.Values of n[P-O] were calculatedusing the EHMoprogram written by Hofimann (1963), the orbital exponentsand diagonal Hiickel matrix elementsgiven in Table 2, and the Wolfsberg-Helmholzparametrization (cl Bartell et al, 1970). The relationship between observedP-O bond length and n[P-O] calculatedusing constant bond lengths(1.50 A), observedO-P-O and P-O-P angles,and an Jp basisset is shownin Figure 1. A plot of observedP-O lengthsversusn[P-O] values calculatedusingthe observedbondlengthsand angles (Fig. 2) givesa statisticallyimprovedcorrelationas expected.Although n[P-O] valuescalculatedusing an spd-basisset also correlatewith P-O bond length .(Bartell et al, 1.970;Lager, 1972), the correlations are not given becausecomparisonsof all electron ab initio scF-Mo and rnnro resultsshow that EHMo calculationstend to over-exaggerate the participation of the d-orbitalsin the resultinguo wavefunctions (LelandAllen, personalcommunication).

B-zn2P2o7 (calvo, 1955b) P(1)-o(1) P(1)-o(2) P(1)-0(3) ?(I)-o(4) P(2)-o(r) P(2)-o(5) P(2)-o(6) P(2)-o(7)

1.s59 1.554 r.s53 1.553 1.s69 r.5s4 t.ss5 t.ss5

0.540 .633 .646 .G46 .640 .633 .646 .646

ca7Ms9(ca'n8)2(Po4)r' (otckme & Eroh' P(1)-o(1) P(1)-0(2) P(r)-0(3) P( r ) - o ( 4 ) P(2)-0(s) P( 2 ) - o ( 6 ) P(2)-o(7) P(2)-o(8) P (3) -o (9) P ( 3 )- o ( r 0 ) P(3)-0(11) P ( 3 )- o ( 1 2 ) P (4) -o(r3) P (4) -0(14) P( 4 ) - 0 ( 1 s ) P (4) -o ( r6) P( 5 ) - O ( r 7 ) P( s ) 4 ( 1 8 ) P( s ) - o ( 1 9 ) P (s)-o(20) P (6) -o ( 2t) P(6){(22) P (6)-0 (23) P( 6 ) - o ( 2 4 ) fler