Maráz, Vilmos

English

Maráz Vilmos

University of Szeged

T H E O R E T I C A L T R E A T M E N T O F B I N U C L E A R C O M P L E X C O M P O U N D S By V. M A R Á Z Institute of Theoretical Physics, The University, Szeged (Received March 15, 1962) The energy levels and transitions of the [ (NH 3 )4Co(OH) 2 Co(NH 3 )4 ] 4 - and of the l (NH3)3Co(OH)3Co(NH 3 )3 ] 3 - binuclear complex ions are calculated by the LCAO-MO method using the half-empirical approximation of W O L F S B E R G and H E L M H O L T Z . The theory of complex compounds has been developed by several authors [1—3] and more recently in [4]. A distinguished group of complexes is represented by the complexes having two or several ions in their centres. In the Institute of General and Physical Chemistry of the University of Szeged the binuclear complex compounds were investigated, hence, their theoretical treatment had to be deve-loped as well. As a matter of fact, in this paper the binuclear complex compounds [(NH 3) 4Co(OH) 2CO(NH 3) 4] 4~ (denoted by K t ) and [ N H j ^ C O I O H ^ C o C N H s y 3 -(in the following K 2 ) are theoretically investigated in detail. The central ions are surrounded by ligands with bi-octahedral symmetry. The two octahedra have in the case of K t a common edge and in the case of K 2 a common face. In fact, the common edges and faces are somewhat contracted, nevertheless, the bi-octa-hedral symmetry is not disturbed in this way. The Co ions are in the centres of the octahedra the OH ion along the common edge and along the common face, res-pectively, furthermore, the N H 3 molecules are on the other vertices of the octa-hedra (Fig. 1 and Fig. 2). The direction of the atomic orbitals of the ligands are denoted on the figures by vectors and the different atoms are labelled by arabic numerals. The ligands may be regarded as electric dipols where owing to the electrostatic attraction of the positive charged central ions the centre of negative charges, i. e. the O and N atoms, is nearer to the Co ions than the centre of the positive charges. For the sake of simplicity, let us suppose that (i) the H atoms of the ligands do not take part in the formation of the complex, therefore, their influences can be neglected; (ii) this is the reason that also the electrons in the closed shells of the Co atoms are not taken into consideration at the fornation of molecular orbitals (MO-s). In fact, we take into account: five 3d, one 4 j and three 4p atomic orbitals of the Co atoms, the three 2p orbitals of the OH ions and O atoms, respectively, finally, the 2pa orbitals of the N atoms of the ammonia molecules along the N-Co bounding axes. Owing to the supposition (t) the 2pn orbitals of N atoms can be 1 * 4 V. MARÁZ neglected. In the course of the calculation wë have observed that in the case of Kx the 2/771 orbitals of the O atoms which are orthogonal to the Co-0 bounding axes do not take port in the bounding, therefore, these atomic orbitals as well as the corresponding two electrons can also be neglected. As a matter of fact, we have Fig. 1 Fig. 2 in the case of K t 30 atomic orbitals and 36 electrons and in the case of K2 33 atomic orbitals and 42 electrons, respectively. The energies of the electrons are calculated by means of the LCAO-MO method, for the extensive simplification of which group theoretical considerations are used [5]. The 30 and 33 atomic orbitals, respectively, mentioned above span the redu-cible representations of the groups considered. Using the character systems of the groups [6, 7] the reducible representations have the form: (KJ ri=7Alg + 7Blu + 4B2g+4B3u + 3B2u+3B3g + B]g + Alu, (K2) T2 = 6E' + 5E"+5Ai+5A'i + A'2. The new basic functions spanning the irreducible subspaces can be found in Table I (K t ) and in Table II (K2). The secular equation having originally the form | / / l 7 — ES{j | = 0 may be bro-ken up into products corresponding in the case of K 1 to the decomposition (K t ) BINUCLEAR COMPLEX COMPOUNDS 5 and in the case of K 2 to the decomposition (K2), respectively. For the calculation of the overlap integrals Sik an approximation method [4] was used; in the case of Co-O bound the nuclear distance 1,88 A , and in the case Co-N bound the nuclear distance 1.92 A was taken into account [8]. The integrals of type Hu were substi-tuted by the ionisation potentials: in the case of the Co atom for 4i orbitals - 7 , 8 4 eV, for 4p orbitals - 4 , 0 8 eV, for 3d orbitals - 9 , 3 8 eV. [9], in the case of N for 2/7<7 orbitals —13,81 eV and in the case of O for 2pcr orbitals —11,24 eV [10], respectively. The integrals Hi} (i ^ j ) were determined by the approximation formula of WOLFSBERG a n d HELMHOLTZ [3]: u p o Hit + Hjj "¡j — ¡j where the empirical factor Fx was chosen as 2,20 for a bounds and 2,65 for n bounds [4]. The energy values are summarized in Table III. Owing to PAUU'S principle the electrons occupy the lowest energy levels, then due to the selection rules, summarized in Table IV, the allowed transitions in Table V can be calculated without any difficulties. The results obtained are in good agreement with those of the experiments [11]. Table I. (K,) CO o N Alg < / = * ( ! ) 2 ) dx2-yl(\) + dx2-y2(2) I( l ) + I(2) pAi)+pA2) p*m+pA2)+p*m+p-{2) P' (1) (2) + P : (3) +PZ (4) PZ (5) -\-PZ (6) -\-PZ (7) +/?! (8) An. dxy(\) + dxy(2) Big dxy(.\)-dxy(2) Blu d;2(l)-d,2(2) dx2 — y^ (1) dx2 — y2 (2) PXW-PA2)-P,W+P:{2) PA1)+PA2)-PAV-PA4) PA5)+PA6)-PAV-PA8) Big dx-_{\)-dx*(2) P A V - P A 2 ) px0)+pA2)-p-.m-p-A2) PA1)-PA2)+PAV-PA4) B2u pAD-py{2) PA5)-PA6)-PA7)+PA8) Big ^yi(l) + DYL (2) PyW+Py(Z) a PA5)-PA6)+PAV-PA8) Biu PAV+PA2) PAV-PAD+PAV-PAV PAD-PA2)-PA3)+PA4) 6 V. MARÄZ Table II. (Ki) Co O N A{ ¿ 2 ( 1 ) + ¿ 2 ( 2 ) P*V)+Pz(2) P*(l)+Py(l)+P*(2) + + Py(2)+Px0)+Py(3) P*W+P.(Z)+P*(3) + +P*W+P.(5)+P,(6) Ai P.0)+P.(2)+P,(3) A» ¿ 2 ( 1 ) - ¿ 2 ( 2 ) i ( l ) - i ( 2 ) Pz(\) —p* (2) P*(Q+PA2)+P*(3)~ - P y ( i ) - P y ( 2 ) - P y ( 3 ) P*W+P*(2)+P*(3)-—Pz (4 ) —Pz(5)—Pz ( 6 ) E' dx2-y2(l) + d*2-y2(2) P * ( l ) + / > * ( 2 ) 2px(l) + 2 p y ( l ) - p x ( 2 ) -- P y ( 2 ) - P x ( 3 ) - P y ( 3 ) P*(2)-P:(3) 2pz (1) + 2pz (4) — px (2) — — Pz(3) — Px (5) — pz (6) />»(2) — P y ( X ) P*(2)+Py(2)-px(3)-py(3) Pz (2) + />z(3) — 2pi (1) (3) (6) —pz (2) — p z (5) E" dxy(\) + dxA2) . d y i ( \ ) + dyi(2) PyW+M 2) p*(2)+py(3)-py(2)-px(3) PA2)+Pz(6)-Pz(3)-Pz(5) ¿2.3 ,2(2) — ¿ 2 - y 2 ( l ) ¿ z ( l ) — dXI(2) p x ( l ) - p x ( 2 ) 2 p y ( \ ) - 2 p x ( l ) + p x ( 2 ) + -\-P* (3) —py(2) —py ( 3 ) 2PZ(\)-2Pz(4)+P*(5) + -\-Pz (6) —pz (2) —Pz (3) Table III. K, Aig Blu B2g Blu Blg A i„ - 3,702 + 8,070 - 0,794 - 3,892 - 4,135 - 4,034 - 9 , 3 8 - 9 , 3 8 - 6,787 - 3,960 - 8,442 - 8,085 - 9,380 - 9,380 - 8,813 — 7,862 - 1 2 , 2 7 4 - 1 1 , 5 6 9 - 1 3 , 8 1 1 - 1 3 , 8 1 1 - 9,806 - 8,466 - 1 4 , 1 9 7 - 1 4 , 1 8 7 - 1 1 , 3 5 3 —11,261 - 1 3 , 9 7 7 - 1 4 , 1 2 6 - 1 4 , 6 6 9 - 1 6 , 7 6 9 K 2 a ; Ai An E" - 4,299 - 10,54 + 8,001 - 4,113 3,987 — 8,295 - 6,063 — 9,086 - 9,084 - 9,616 - 9,467 - 9,38 - 9,38 - 1 2 , 6 0 3 — 11,402 - 1 0 , 4 9 4 - 1 1 , 6 2 2 - 1 4 , 5 7 6 - 1 4 , 7 2 5 - 1 1 , 3 2 9 - 1 4 , 1 2 1 - - 14,079 B I N U C L E A R C O M P L E X C O M P O U N D S 7 Table IV. Table V. к , Alg-> -Б lu A\g-< *-Ü2u Alg * В lu A'tu-—-Bi0 A,u+—B2g Alu- •'Big Big * *-Blu Big • Blu Big < * > Blu Bzu*-*B,g Blu* Big Blu* •Big К2 .. A't^AÏ A'i -*—*Е' . Е'^Е' Al — Я" А\-—-Е' 5 817 23 939 40 898 44940 8 189 26 375 41 568 45 594 8 746 26 948 42 479 46 925 10 376 28 086 42 544 47 417 11 667 28 199 42 568 47 579 12 748 29 296 43 464 48 103 15 983 29 869 44 246 48 668 21 018 32 644 44 432 48 991 21 341 32 757 44811 49 846 21 913 39 462 44 852 50 475 к 2 8 754 18 113 40 285 44 214 9 456 20 461 . 4 0 301 44 295 11 360 20 477 40 624 4 4 4 0 0 11376 24 479 40 640 44 852 11 731 25 068 40 995 45 513 17 742 26 762 41 697 46 667 17 895 28 376 42 496 49 983 18 097 28 667 43 512 51484 :: The author wishes to express his thanks to dr. F. J. G I L D E for calling his atten-tion to the problem investigated and for the helpful discussions. •References [1] Ilse, F. E., H. Hartman: Z. phys. Chem. 197, 239 (1951). [2] Pauling, L.: The Nature of the Chemical Bond (Cornell University Press, New York, 1939). f Wolfsberg, M., L. Helmholtz: J. Chem. Phys. 20, 837 (1952). Gilde F.: Dissertation, Szeged, 1958. Wigner, E.: Gruppentheorie und ihre Anwendung (Vieweg, Braunschweig, 1931). [6] Éyring, H., J. Walter, G. E. Kimball: Quantum Chemistry (Wiley, London, 1944). [7] Herzberg, G.: Molekula-színképek és molekula-szerkezet II. (Akadémiai Kiadó, Budapest, 1959), p. 142. [8] Pauling, L.: The Nature of the Chemical Bond (Cornell University Press, New York, 1939), p. 167, 169. [9] Landolt, Bó>«iíeí'n:Zahlrenwerte und Funktionen. Atom und Molekularphysik I (Springer, Ber-lin, 1954). [10] Mulliken, R. S.: J. Chem. Phys. 2, 792 (1934). [llj Császár J.: Private communication. ТЕОРЕТИЧЕСКОЕ И С С Л Е Д О В А Н И Е Д В У Я Д Р Р Н Ы Х КОМПЛЕКСНЫХ ИОНОВ В. Mapas Были рассчитаны электронные энергии двуядерных комплексных ионов [(NH 3 )4Co(OH)2Co(NH 3 )4] 4 - И [ ( N H 3 ) 3 C o ( O H ) 3 C o ( N H 3 ) 3 p -с помошью полуэмпирического метода МО-ЛК.АО. 

Theoretical treatment of binuclear complex compounds

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Theoretical treatment of binuclear complex compounds

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