Maráz, Vilmos

English

Maráz Vilmos

University of Szeged

LFMO TREATMENT OF BINUCLEAR COBALT COMPLEXES By V. MARÁZ Institute of Theoretical Physics, Attila József University, Szeged (Received July 10, 1975) In this paper the energy levels and electron transitions of the [(NH^iCoCOH^CoCNH,,),,]4-1-and [(NH3)3Co(OH)3Co(NH3)3]3+ binuclear complex ions are calculated by the LFMO method (ligand field method combined with LCAO-MO method). Introduction As well known, the ligand field (LF) method (BETHE [1], VAN VLECK [2]) is a fairly good approximation for the interpretation of some important properties of complex compounds having only one central metal ion. As known, this method treats the ligands as point charges or point electric dipoles and considers the electrons of the central metal ions as if they were subjected to an electric field originating from the surrounding atoms or molecules. Since the first application of the LF method [2] many authors dealt with this method and employed it to calculate the electronic structure, transitions, magnetic properties etc. of such complexes, and several excellent books have been published on this topic. (ILSE and HARTMANN [3], BALLHAUSEN [4], JORGENSEN [5], GRIFFITH [6], ORGEL [7], MOFFITT [8], LIEHR [9], TANABE and SUGANO [10], Kiss [11], GILDE and BAN [12] etc.) It is evident that the LF method cannot be applied in itself in the case of poly-nuclear complexes, but the basic idea of the method is applicable in this case, too, if we combine this method with other methods, for example the LCAO-MO method. In the following we call this method LFMO method and we treat the binuclear complex ions [(NH3)4Co(OH)2Co(NH3)4]4+ and [(NH3)3Co(OH)3Co(NH3)3]3+ (denoted in the following by Kx and K2, respectively) by this method. Geometries and method of calculation We assume that the geometry of the complex ions Kx and K2 is "bi-octahedral": the two octahedra have in the case of ^ a common edge and in the case of K2 a common face, and on the basis of Pauling's ions radii [13] we take the nuclear distance Co—O to be 1.88 A, Co—N 1.92 A and Co—Co 2.66 A for both complexes. The symmetry of these systems is D2h(AT1) and D3h(A"2). l* 86 V. MARÁZ In the present paper we treat these complex ions by the LFMO method: (1) because of the undoubted importance of the bridges we treat the compounds Co(OH)2Co and Co(OH)3 Co by the LCAO-MO method (zeroth order problems), (2) then, we take into account the NH3 molecules as point electric dipoles (having 1.48 Debye dipole moment) setting up an electrostatic field around the central compounds. After K. J0rgensen [5] we call this field "Iigand field". Zeroth order problems In the LCAO—MO treatment of Co(OH)2Co and Co(OH)3Co we neglect the influences of the H atoms on the compounds and we do not take into account the electrons in the closed shells of Co and O atoms. We take into account only the six valence electrons of the Co ions and the four valence electrons of the OH ions (20 electrons for Kt and 24 electrons for K2). For the calculation of MO-s we take into account the five 3d, one 4s and three 4p atomic orbitals of Co atoms and the three 2p orbitals of O atoms and we represent these atomic orbitals by Slater type orbitals. Table I (AT,) Co o dx2_yi(l) + dx2_y2(2) »(l) + *(2) PAV+PÁ2) P*(l)+PyQ)+P*Q.)+Py<?) u dxy(\) + dxy{2) Bia dxy(\)~dxy{2) PAD+PÁ2) Blu </xi(l)-</,,(2) dxi_y2(X)-dxi_yi(l) j (1 ) - Í (2 ) PÁV-PÁ2) -PÁD+PyO)-PÁ2)+py(2) dXz(l) — dXI(2) PAD-PÁ2) -PM+Py0)+Px(2)-Py(2) Btu py{\)-py(2) PAV-PA2) Py(D+Py(2) B3u dXI(l)+dxz(2) PAD+PA2) PM)+PAD-PA2)-Py(.2) LFMO TREATMENT OF BINUCLEAR COBALT COMPLEXES 87 From these atomic orbitals we can easily construct symmetry adapted functions transforming according to the irreducible representations of D2b and D3h using group theoretical considerations. The reducible representations are A = 5AH+5Blu + 3B2g+3B2a + 3B3u+2BSg+2Blg+Alu r2 = 5E'+4E"+4A'1+4A2+A2. The symmetry adapted functions are presented in Table I. Table I (K2) Co o dzl(l) + dz2(2) »(1) + 5<2) PÀD+PA2) (1) +Py (1) +Px (2) + +py(2)+px(3)+py(3) ' A't PM+P,(2)+P,Q) At J(1)-«(2) PAD-PA2) PA\)+PA2)+PxQ)~ -py(\)-py{2)-py(S) E' dxi_yi(\) + dxi_yi(2) Px(\)+Px{2) — 2px(X) — 2py(\)+px (2) + +py(2)+px(3)+py(3) p,(3)-p,(2) dxy(l)-dxy( 2) dyi{2)-dyi{\) py(2)-py(l) Px (2) +Py (2) —px (3) —py (3) /».(2)+/».(3)-2p,( l) dxy(l) + dxy(2) dyi(l) + dyi(2) PyV)+Py(2) px(.2)+py(.3)-py(2)-pxQ) E dx2_yi(2)-dx2_y2(l) dx,(D-dxA2) 2px(\)-2py{\)~ -px( 2) -px(-3) +py(2) +py( 3) For the secular equations we calculated the group overlap integrals StJ exactly, while the group integrals Htj (i^j) have been determined by the approximation formula of WOLFSBERG and HELMHOLZ [14] HTJ = 0,5 KS I J (HA + H J J ) where the empirical factor K was chosen to be 2.20 for a bonds and 2.62 for n bonds [15]. The integrals HH were substitued by ionization potentials: in the case of Co, for 4s orbitals —7.84 eV, for 4p orbitals -4 .08 eV, for 3d orbitals -9 .38 eV [16] and in the case of O, for 2pt7 orbitals -11 .24 eV and for 2pn orbitals -10 .54 eV [17]. The energy values (in eV) and the LCAO coefficients of the normalized MO-s are summarized in Table II. 88 .. Table II (KJ symmetry energy ci c 3 «S A ig - - 3 . 4 2 5 -- 8 . 2 0 8 - 9 . 4 4 1 - 9 . 7 9 9 - 1 3 . 0 4 0 - 0 . 0 5 9 138 0 . 6 6 5 6 6 6 - 0 . 2 9 2 0 5 5 - 0 . 6 0 3 2 6 4 0 . 3 4 7 4 6 2 - 0 . 0 4 3 3 4 9 0 . 2 3 5 7 7 0 0 . 9 5 4 3 0 4 - 0 . 1 7 7 3 2 8 0 . 0 4 8 3 2 0 0 . 2 8 4 8 3 6 0 . 5 2 2 1 8 0 0 . 0 1 4 8 9 4 0 . 7 8 3 8 7 5 0 . 3 7 1 0 7 8 1 .052 6 1 6 0 . 1 6 8 0 0 7 - 0 . 0 0 6 9 8 5 - 0 . 0 4 8 0 4 9 - 0 . 1 1 9 7 3 4 0 . 3 9 8 0 7 3 . - 0 . 6 3 1 5 5 4 0 . 0 5 7 6 1 6 - 0 . 1 7 7 0 2 6 0 . 7 0 4 6 1 1 Ai,, - 9 . 3 4 3 1 Bi. - 8 . 5 5 0 - 1 1 . 8 4 3 0 . 9 0 2 0 9 7 - 0 . 4 3 9 9 0 3 0 . 5 1 5 110 0 . 8 6 1 3 7 7 B,u + 4 0 . 6 4 0 - 5 . 4 6 6 - 8 . 2 3 7 - 9 . 0 5 4 - 1 2 . 4 4 9 - 0 . 2 8 9 141 - 0 . 1 0 8 2 3 0 - 0 . 5 0 0 1 3 8 0 . 8 3 7 761 0 . 1 4 2 5 4 2 - 0 . 0 8 6 190 0 . 2 1 7 0 0 3 0 . 7 4 1 2 8 9 0 . 5 1 9 545 - 0 . 3 8 2 2 4 9 - 0 . 1 4 6 6 3 7 0 . 4 8 5 199 - 0 . 2 0 1 0 4 1 - 0 . 1 0 0 7 7 3 - 0 . 1 6 0 9 2 3 0 . 1 4 3 2 8 9 0 . 5 3 9 3 3 7 - 0 . 1 2 2 9 4 1 0 . 0 3 3 4 7 9 - 0 . 0 0 6 4 0 4 - 0 . 5 2 3 6 7 0 0 . 3 5 7 385 0 . 4 0 9 5 9 5 0 . 0 7 9 291 0 . 8 1 1 2 7 7 Blg + 2 . 7 0 1 - 8 . 1 7 5 - 1 2 . 4 1 6 - 0 . 3 4 3 6 8 4 0 . 8 7 3 4 9 8 0 . 4 0 9 138 1 .023 2 8 6 0 . 2 9 8 0 0 7 - 0 . 1 3 0 174 0 . 6 2 5 7 0 3 - 0 . 3 9 0 9 6 3 0 . 7 9 9 2 6 2 Btu - 3 . 8 1 0 - 8 . 6 1 3 - 1 2 . 4 3 2 - 0 . 0 7 5 0 4 1 0 . 9 0 1 8 0 0 0 . 4 3 9 4 0 6 0 . 9 8 7 295 0 . 2 0 2 4 2 2 - 0 . 1 8 3 9 8 2 0 . 4 6 8 2 9 9 - 0 . 4 5 9 0 3 6 0 . 7 9 2 9 7 8 - 1 .899 - 9 . 1 2 4 - 0 . 1 3 9 5 5 6 0 . 9 9 2 2 2 3 0 . 9 9 9 0 4 0 0 . 0 7 6 8 0 0 B3u - 5 .264. - 7 . 7 4 2 - 1 2 . 2 3 0 0 . 1 4 8 135 0 . 8 5 4 178 - 0 . 5 2 8 837 0 . 9 9 5 703 - 0 . 1 1 3 3 4 0 0 . 0 1 8 591 0 . 0 1 4 2 1 5 0 . 6 7 1 4 2 5 0 . 7 6 2 123 Table II (K2) symmetry energy ci «a c 3 ci cb AÍ - 2 . 4 7 0 - 7 . 4 6 7 - 9 . 7 6 3 - 1 3 . 1 5 5 - 0 . 1 5 5 6 9 5 0 . 6 1 2 587 0 . 6 9 5 179 0 . 3 7 5 0 0 6 r 0 . 1 6 7 135 0 . 6 1 8 8 9 0 - 0 . 7 3 7 7 8 6 0 . 3 9 4 7 8 4 d. 102 8 5 0 0 . 3 2 9 7 6 2 0 . 0 4 3 9 7 1 - 0 . 1 2 8 6 7 0 0 . 5 7 3 7 5 8 - 0 . 6 1 7 8 8 0 0 . 1 2 0 5 9 5 ; 0 . 6 4 4 2 5 3 А'г - 1 1 . 3 0 8 1 a; + 4 7 . 7 0 2 - 5 . 3 9 4 - 8 . 7 3 0 - 1 2 . 1 2 1 0 . 2 9 0 3 2 6 - 0 . 1 2 1 4 0 4 0 . 9 6 2 781 - 0 . 2 1 4 0 5 4 1 .559 7 4 8 0 .491 707 0 . 0 5 6 2 2 3 0 . 2 2 9 541 - 1 . 4 9 2 8 0 5 0 . 5 6 1 751 0 . 0 9 4 8 6 0 0 . 0 1 0 192 - 0 . 6 5 0 8 3 9 - 0 . 3 2 9 8 3 9 0 . 2 2 4 5 0 6 0 . 8 7 5 8 3 5 E' - 4 . 0 8 2 - 7 . 7 7 2 - 8 . 9 4 2 - 11 .9S7 - 12.491 - 0 . 1 2 7 2 2 4 0 . 1 5 0 743 0 . 9 2 0 6 6 3 0 . 3 1 8 4 2 8 0 . 1 3 7 8 3 4 - 0 . 0 4 3 8 3 0 0 .861 337 - 0 . 1 7 8 2 9 2 - 0 . 1 2 1 4 2 0 0 . 4 8 7 7 1 5 0 . 9 8 0 3 2 6 0 . 1 6 2 7 1 4 0 . 1 5 5 195 - 0 . 1 2 5 0 3 7 - 0 . 1 1 2 4 4 9 0 . 0 7 0 7 1 4 - 0 . 5 0 8 9 7 1 0 . 2 6 7 9 2 4 - 0 . 6 2 9 115 0 . 5 4 1 9 1 1 0 . 4 3 5 881 - 0 . 3 3 1 7 7 4 - 0 . 2 6 4 2 7 6 0 . 6 2 3 291 0 . 5 3 7 6 1 8 E" + 1 .622 - 7 . 8 5 6 - 9 . 2 5 0 - 12 .554 - 0 . 1 4 7 161 0 . 5 4 4 901 0 . 7 7 5 6 1 0 - 0 . 3 0 6 4 3 2 - 0 . 3 0 7 561 0 . 6 6 3 5 9 6 - 0 . 6 2 7 0 4 4 - 0 . 3 2 8 9 7 4 1 .003 7 0 8 0 . 3 0 4 0 4 0 - 0 . 0 3 1 2 9 5 0 . 1 0 6 6 8 6 - 0 . 5 7 0 871 0 . 4 5 5 551 0 . 0 4 4 3 6 2 0 . 7 8 2 2 1 0 LFMO TREATMENT OF BINUCLEAR COBALT COMPLEXES 89 Ligand field potentials The electrostatic potential of the ligand fields can be written in the form $(?) = — ¿P;grad|r —rf|-1, ¡=1 where n is the number of the point dipoles, rt and pt is the position vector and the dipole moment of the /-th dipole. By means of the well known formula [18] ... r12 MmÄ,2l+l rl+ where r< is the lower and is the higher of ry and r2, the ligand field potentials can be expressed in terms of spherical harmonics. Because of the approximations applied in the calculations it will be convenient to expand $ in the form 1 4n * = - Z 2 2TT 1 = 0 m--I ¿l-r r \ 2 Pi g rad Ylm(ß, cp) 1 ^ ( 3 , , cpt) ' Id) r> 'Î.<Pj)]}. + . + 2 Pj grad (p') Yl*(9 (a) L r > where the first summation is extended over the dipoles near Co1; the second is exten-ded over the dipoles near Co2 and {r, 3, <p}; {/-¡, cp,} are coordinates referred to Co! as origin and {/•', 9', <p'}, {r'j, <pj} are coordinates referred to Co2 as origin. As the dipoles are all directed radially toward the corresponding central ion and all dipoles have the same extent Q?) of dipole moment both members of the expression of <t> can be written in the form where $=-Z 2 Bi(r)Ylmß,<P) l = Om=-l Rlm{r) 4n 2 7 + 1 . * 471 2 / + 1 lprl-12rrl-1Vm(9l.<PÙ if 0 S r S r , I ( l + l ) p r r l - * 2 r } K ( P i , 9 d if r ^ r s -In the case of Kt and K2 r,=r0=1.92A, and 91 = 92=45°, 95=96=90°, ^ = 0 , <p2=m°, (p5=-(pe=90° for Ku and S1=S2=S8=45°,- «p^lSO0, <p2=-<p3=60° for K2. The potential energy of an electron in the ligand field is of course V= —e<P. Energy levels and transitions According to the perturbation theory, for the calculation of the energy levels in first order the matrix elements ,(I/'|V|I¡/) must be calculated with the zeroth order MO-s. As these MO-s are built up from Co and O atomic orbitals, these matrix elements are multicentre integrals. In the calculations we neglected all the two- and ! 90 V. MARÁZ three-centre integrals and took into account only the single-centre integrals. (For this reason the potential 4> has been written in two terms.) With this approximation we get the values for the first order energies (in eV) summarized in Table III. The wavenumbers (in cm - 1 ) of the allowed electron transitions are presented in Table IV. Table 111 * «1 2 - 5 . 7 8 7 - 9 .415 - 2 . 1 0 4 - 1 1 . 3 0 8 - 6 . 1 9 4 - 9 .441 - 2 . 2 2 0 - 1 1 . 5 3 3 - 6 . 8 2 8 , - 11 .862 - 6 . 5 9 2 - 1 1 . 8 9 7 - 7 . 1 9 0 - 1 2 . 1 1 1 - 7 . 3 6 8 - 1 2 . 4 6 5 - 7 . 7 9 8 - 1 2 . 2 4 3 - 7 . 7 6 9 - 1 2 . 4 9 8 - 8 . 3 1 5 - 1 2 . 2 5 0 - 8 . 1 8 2 - 1 2 . 9 7 9 - 8 . 6 2 9 - 1 2 . 3 1 9 - 9 . 0 3 8 - 8 . 8 3 0 - 12.604 - 9 . 4 2 0 - 9 . 1 1 1 * In this table only the negative energies are summarized. Table IV I 10 588 32 784 9 9 9 3 36 539 13 0 4 3 34 607 10 2 4 0 37 8 9 2 15 495 36 4 7 2 13 4 7 4 38 7 0 3 16 150 38 776 16 559 39 867 17 9 5 0 41 379 19 738 41 127 21 0 8 3 4 2 628 2 2 8 2 3 41 394 21 267 4 3 6 8 3 3 0 369 4 2 8 0 2 2 4 550 4 3 748 31 778 4 5 269 2 8 6 1 4 47 745 33 304 47 390 2 9 156 4 8 804 34 8 2 8 47 6 5 7 2 9 217 . 48 865 Comparing these results with other calculations [19] and the experimental ab-sorption spectra of the complexes [20] we can say that the results of the transitions are acceptable and they reproduce the main electronic bands of the complexes fairly well. However, this method is in consequence of his nature, incapable to repro-duce many other properties, as for example the charge transfer states. These other properties can be interpreted with other methods as for example with the extended Wolfsberg—Helmholz method [21]. * * * The author wishes to express his thanks to Dr. F. J. GILDE, Director of the Institute of Theoretical Physics, for helpful discussions and to Dr. GY. PAPP for his assistance in the computations. These computations were performed on the MINSZK—22 computer of the Attila Jozsef University. LFMO TREATMENT OF BINUCLEAR COBALT COMPLEXES 91 References [1] Bethe, H.: Ann. Physik 5, 3, 135 (1929). [2] Van Vleck, J. H.: The Theory of Electric and Magnetic Susceptibilities (Oxford University Press, Oxford and New York, 1932) [3] Ilse. F. E„ H. Hartmarm: Z. physik Chem. 197, 239 (1951). [4] Ballhausen, C. J.: Introduction to Ligand Field Theory (McGraw-Hill, New York, 1962) [5] Jergensen, C. K.: Orbitals in Atoms and Molecules (Academic Press, London and New York, 1962) [6] Griffith, J. S.: The Theory of Transition Metal Ions (Cambridge University Press, London, 1961) [7] Orgel, L. E.: An Introduction to Transition Metal Chemistry (John Wiley and Sons, Inc., New York, 1960) [8] Moffith, W.: J. Chem. Phys. 25, 1189 (1956). [9] Liehr, A. D.: J. Phys. Chem. 64, 43 (1960). [10] Tanabe, Y„ S. Sugano: J. Phys. Soc. Japan 9, 753 (1954). [11] Kiss, A.: Acta Chem. et Phys. Szeged 3, 6 (1950). [12] Gilde, F. J. and M. I. Bán: Acta Phys. Chem. Szeged 5, 3 (1959) [13] Pauling, L.: The Nature of the Chemical Bond (Cornell University Press, New York, 1939) [14] Wolfsberg, M., L. Helmholz: J. Chem. Phys. 20, 837 (1952). [15] Gilde, F.: Dissertation, Szeged, 1958. [16] Landolt-Börnstein: Zahlenwerte und Funktionen. Atom und Molekularphysik I. (Springer, Berlin, 1954) [17] Mulliken, R. S.: J. Chem. Phys. 2, 792 (1934). [18] Condon, E. U. and G. H. Short ley: The Theory of Atomic Spectra (Cambridge University Press, London and New York, 1953) [19] Maráz, V.: Acta Phys. et Chem. Szeged 20, 5 (1974). [20] Császár, J.: Private communication [21] Ballhausen, C. J. and H. B. Gray: Inorg. Chem. 1, 111 (1962). ИССЛЕДОВАНИЯ ДВУХЪЯДЕРНЫХ КОМПЛЕСКОВ КОБАЛЬТА МЕТОДОМ ЛПМО В. Мараз В данной работе рассчитаны энергии состояний и электронных переходов двухъядерных комплексных молекул [(ЫН3)4Со (ОН)2Со(КН3)4]4 + и [(№1з)3Со(ОН)8Со^Н3)8]3+ с помощью метода ЛПМО (метод лигандного поля с ЛКАМО). 

LFMO treatment of binuclear cobalt complexses

http://acta.bibl.u-szeged.hu/23956/1/phys_chem_021_fasc_003_004_085-091.pdf

LFMO treatment of binuclear cobalt complexses

Abstract

Similar works

Full text

Available Versions

University of Szeged