Maráz, Vilmos

English

Maráz Vilmos

University of Szeged

SEMI-EMPIRICAL MOLECULAR ORBITAL CALCULATIONS OF BINUCLEÁR COBALT COMPLEXES, II By V. MARÁZ Institute of Theoretical Physics, Attila József University, Szeged (Received July 10, 1975) In this paper the energy levels, molecular orbitals, orbital populations and transitions of the [(NHj)iCo(OH)2Co(NH3)J4 + and of the [(NH3)3Co(OH)3Co(NH3)3p+ binuclear complex ions are calculated by the LCAO-MO method using the half-empirical formula of Wolfsberg and Helmholz [1]. Introduction In a previous paper [2] we investigated theoretically the binuclear complex compounds [(NH3)4Co(OH)2Co(NH3)4]4+ (denoted in the following by Kj) and [(NH3)3Co(OH)3Co(NH3)3]3+ (K2), and we calculated the energy levels, molecular orbitals, orbital- and bond overlap populations and transitions of these complex ions by a simple semi-empirical LCAO—MO method. In these calculations we neglected not oiity the influences of the H atoms and thé electrons in closed shells on the complex compounds but'the interactions between ligands OH and NH3 , too. In the present paper because of undoubted importance of the bridges we take into account besides metal-metal interactions the interactions between ligands OH but we neglect the interactions between NH3 . The method of the calculations and the geometries of the complex ions are the same as in the paper [2]. The computations were performed on the MINSZK—22 computer of the Attila József University. Results and discussion The energy values of the MO's are summarized in Table I. These energies differ from the energies in [2] only a little (0.1—0.2 eV) with the exception of the symmetry A2 (K2) where the difference is 0.8 eV. In the ground state of the complexes the highest filled MO of Kx is 2b2u ( -8 .557 eV), that of K2 is 3e" ( -9 .207 eV), the lowest empty MO-s are 16lg and 3e', respectively, as in [2]. The wavenumbers of the allowed electron transitions were calculated by means of Bohr's frequency rule the most important wavenumbers of which are summa-rized in Table II. In this table we give the wavenumbers of those transitions which were also taken into account in the paper [2]. The difference between the two sets of wavenumbers is not too high except the transition 26lg*-263u where the difference is 4500 cm-1 . 94 V. MARÁZ Table I B3u B t u *30 ^lu - 0 . 2 7 2 + 59 .191 + 3 . 9 6 3 - 3 . 3 6 4 - 1 .705 + 1.881 - 8 . 5 5 0 - 9 . 3 4 3 - 5 . 9 9 8 - 1 .418 - 6 . 0 1 4 - 7 . 1 2 2 - 8 . 5 5 7 - 9 . 1 1 0 - 1 1 . 8 4 3 - 6 . 9 0 2 - 5 . 9 0 8 - 1 2 . 2 4 5 - 1 1 . 7 5 7 - 1 2 . 3 6 0 - 1 4 . 1 3 6 - 9 . 2 8 1 - 8 . 3 3 5 - 1 4 . 7 1 9 - 1 4 . 7 5 2 - 1 4 . 1 1 1 - 1 2 . 7 3 6 - 1 2 . 1 8 1 - 1 4 . 8 8 6 - 14 .794 - 1 5 . 3 3 4 - 1 5 . 2 0 9 aí M Al F E' + 1 .215 - 1 1 . 3 0 8 + 4 8 . 9 8 6 - 2 . 9 8 5 + 2 . 3 8 9 - 5 . 5 3 3 - 0 . 3 1 5 - 6 . 7 7 9 - 5 . 9 4 6 - 9 . 4 6 5 - 8 . 4 8 3 - 8 . 7 6 0 - 9 . 2 0 7 - 1 2 . 7 4 5 - 1 1 . 9 6 1 - 1 1 . 7 8 4 - 1 2 . 3 1 2 - 1 5 . 1 9 4 - 1 4 . 9 2 4 - 1 2 . 3 6 5 - 1 4 . 6 7 9 - 1 4 . 6 7 9 Table II K 9 7 6 3 3 2 6 8 5 9 5 6 8 8 2 4 3 9 9 13 353 2 7 2 1 4 5 8 4 2 2 6 311 17 4 2 0 3 8 0 9 0 7 9 2 3 36 541 2 0 6 4 7 3 9 172 19 5 9 0 40 382 2 5 835 4 6 3 3 6 2 0 5 5 8 4 7 103 2 5 875 4 6 4 6 5 21 6 7 2 4 8 531 Table III atom orbital Ki K, 3 dxy 1 .2258 0 . 9 6 8 8 3 dx, 0 . 6 4 1 9 0 . 7 9 8 8 3 dy, 1 .9939 0 . 7 9 8 8 0 . 7 9 5 2 0 . 9 6 8 8 Co 3 dz% 0 . 8 3 0 5 0 . 9 0 5 7 4 j 0 . 5 5 4 1 0 . 7 6 1 0 4 p x 0 . 1 5 6 0 0 . 1 6 7 9 4 P y 0 . 2 2 5 7 0 . 1 6 7 9 4P, 0 . 1 7 8 5 0 . 2 6 3 8 2px 1.4997 1 .5513 o 2Py 1 .4997 1 . 5 5 1 3 2Pl 1.6935 1 . 6 5 2 5 N 2p. 1 .6866 1 . 6 8 8 5 SEMI EMPIRICAL MOLECULAR ORBITAL CALCULATIONS OF BINUCLEAR Co COMPLEXES 9 5 The orbital populations [3] of the complexes are also similar in the two calcula-tions (Table III.) and the resultant electron configurations of Co atoms according to the present calculations are (3<05-5 (4i)0-6 (4p)0-6 for and (3d)** (4sf 8 (4pf * for K2. The calculation shows that we obtain reasonable results for polinuclear complex compounds if we disregard the interactions between the ligands of the complexes. * * * The author wishes to express his thanks to Dr. F. J. GILDE, Director of the Ins-titute of Theoretical Physics, for his helpful discussions and to Dr. G Y . P A P P for his assistance in the computations. References [1] Wolfsberg, M„ L. Helmholz: J. Chem. Phys. 20, 837 (1952). [2] Maráz, V.: Acta Phys. et Chem. Szeged 20, 5 (1974). [3] Fraga, S., G. Malii: Many-Electron Systems: Properties and Interactions (W. B. Saunders Com-pany, Philadelphia, London and Toronto, 1968) ПОЛУЭМПИРИЧЕСКИЕ ВЫЧИСЛЕНИЯ НА ДВУХЪЯДЕРНЫХ КОМПЛЕКСАХ КОБАЛЬТА МЕТОДОМ МОЛЕКУЛЯРНЫХ ОРБИТ II. В. Мараз В данной работе рассчитаны энергии, молекулярные орбиты, орбитальные популации и электронные переходы с помощью метода ЛКАО-МО с использованием полуэмпири-ческой формулы Вольфсберга — Гельмгольца. 

Semi-empirical molecular orbital calculations of binuclear cobalt complexes 2.

SEMI-EMPIRICAL MOLECULAR ORBITAL CALCULATIONS OF BINUCLEAR COBALT COMPLEXES By V. M A R Á Z Institute of Theoretical Physics, Attila József University, Szeged (Received December 15, ¡973) In this paper the energy levels, molecular orbitals, orbital and bond overlap populations and transitions of the [(NH3)4Co(OH)2Co(NH3)4]4 + and of the [(NH3)3Co(OH)3Co(NH3)3]3+ binuclear complex ions are calculated by the LCÁO-MO method using the half-empirical formula of W O L F S B E R G a n d H E L M H O L T Z . The binuclear complex compounds [(NH3)4Co(OH)2Co(NH3)4]4+ (denoted in the following by KJ and [(NHa^CoCOH^CoCNHgy3"1- (K2) are theoretically in-vestigated by a simple semiempirical LCAO-MO method. In these complexes the central cobalt ions are surrounded by ligands of approximately "bi-octahedral" symmetry (D ih and Dsh). The two octahedra have in the case of K^ a common edge and in the case of K2 a common face. The Co ions are in the centres of the octahedra, the OH ions are along the common edge (K^) and along the common face (K2), and the NH 3 molecules are on the other vertices of the octahedra. If we disregard the distortions of the octahedra on the basis of Pauling's ions radii [1] we obtain 1,88 A , 1,92 A and 2,66 A for the bond distances of Co-O, Co-N and Co-Co bonds, respectively. Computational details In the calculations we neglect the influences of the H atoms on the complex compounds and we do not take into account the electrons in the closed shells of Co, O and N atoms, taking into account only the six valence electrons of the Co ions, the four valence electrons of the OH ions and the two valence electrons of the NH 3 molecules (36 electrons for each of both complexes). For the LCAO-MO treatment of complex ions we take into account the five 3d, one 4s and three 4p atomic orbitals of Co atoms, the three 2p orbitals of O atoms and one 2p orbital of N atoms. The 2 p and 3d atomic orbitals are represented by SLATER type orbitals, arid the radial wave function of 4s, 4p orbitals is approximated by 4 "Aapprox = Z C k r k e ~ a r k=l where a=2.60 and ^ = -0 .047 530 507 c2 = 0.360145 640 c3 = 0.728 294 860 -c4 = - 0 . 0 4 1 616865 / 6 V. MARÁZ The coefficients ck are calculated from the equation • / ("/'-'/'appro ¿ fdx = min. where ip is a SLATER type 4s, 4 p radial wave function. The energy levels and molecular orbitals have been calculated by means of group theoretical considerations, which give Fx = lAlg + 1BXU + 4B2g + 4 B3u + 4Bou + 3 B3g + 2 Blg + Alu r2 = 6E' + 5E" + 5A[ + 5A: + A'z reducible representations for the complexes. The bases of the irreducible repre-sentations are presented in Table I. The group overlap integrals S)j have been calculated exactly, the group integrals Table I (A',) Co o N Alg dlt{\) + d_*_(2) dx,_y,W+dxi_y,{ 2) P,W+Py(.l)+Px(2)+Py(2) PAÙ+PAV+PAV+PA*) dxy(\) + dxy{l) Blg dxyW~dxy{2) PAD+PA2) Blu • dx,^,{\)~dxi_y,{ 2) • / > = ( D - / > = ( 2 ) -pJY)+py(Y)-pJ2)+py(2) PAV+PAV-PAD-PA*) Pz Í5) +p, (6) —/>. (7) —p, (8) dxA\)~dxz{2) PAV-PAV -pA\)+py(l)+px(2)-py(2) PAV-PAV+PAD-PA*) Siu dyz0)~dyz(2) py{\)~py{2) pz(\)-pA2) PA5)-PA6)-PzO)+PA$) B3g dyz(i) + dyz(2) py(.\)+py{2) PA5) ~PZ (6) +pz (7) - / > , (8) 5 3 „ dxz(l)+dXA2) PAD+PA2) px(\)+py(\)-px{2)-py{2) PA\)-PA2)-PAT>)+PA4) 7 V. MARÁZ: MOLECULAR ORBITALS OF BINUCLEAR COBALT COMPLEXES Table I (K2) Co o N A{ ¿ . 2 ( l ) + rf22(2) i ( l ) + i ( 2 ) p.A\)+pz(2) Px{\)+Pyw+Px(2) + +py(2)+px{?)+py(y) Pz(X)JrPA2)+Pz(3) + +/>z(4) 4 \P Z (5 ) +p-(6) AÍ A'i dz,{\)-dz,{2) • í ( 1 ) - J ( 2 ) PÂV-PÂ?) px(l)+px(2)+px(3)-~py(i)-py(.2)-py(3) -PA\)+PA2)+PAV--PÁ4)-PA5)-PÁ6) E' ( D + d , « - , " ® dxzm + dxt(2) Px(l)+Px(,2) — 2px(l) — 2py ( 1) +px (2) + +py(2)+px(3)+py(3) pA3)-PÁ2) pz(2)+pz(3)+pz(5) + +PJ6)-2pM)-2PA4) dxy{l)-dxy{2) dyz(2) — dy.(l) Py{2)-py{\) px (2)+Py (2) —px (3) —py (3) pz{2)+pz(3)-2pz{\) PA3)+PA6)-PA2)-PA5) E" dxy{\)+dxy{2) dyz(l) + dyz(2) py(l)+py(2) px(2)+py(3)-py(.2)~px(3) PA2)+PA<S)-PÂD-PÂ5) dx2_y-{2)-dxi_yi(\) dxz(l)~dxz(2) • px(\)—px(2) 2px( l ) — 2py(X) — ~px(2) px (3) +py (2) +py (3) Pl(2)+pjy)-pj5)--Pz(6)-2PA1) + 2PA4) H i j i i r j ) have been determined by the approximation formula of W O L F S B E R G and H E L M H O L T Z [2] Hu = 0 ,5 FxStj(Htt + H j j ) ; where the empirical factor Fx was chosen to be 2.20 for a bonds and 2.62 for n bonds [3]. The integrals Hit were substituted by the ionization potentials: in the case of Co ions for 4s orbitals — 7.84 eV, for 4p orbitals —4.08 eV, for 3d orbitals —9.38 eV [4], in the case of NH 3 molecules for 2p orbitals —13.81 eV and in the case of OH for 2pa orbitals -11 .24 eV and for 2pn orbitals -10 .54 eV [5], respectively. Results and discussion The energy values of the MO's are summarized in Table II. The 36 electrons occupy these energy levels according to Pauli's principle. In the ground state of the complexes the highest filled MO of Kx is 2b2u ( -8 .357 eV), that of K% is 3e" (—9.208 eV). The lowest empty MO's are 1 blg and 3e', respectively. On the basis V. MARÁZ cm" — Fig. 1 crr,' Fig. 2 9 V. MARÁZ: MOLECULAR ORBITALS OF BINUCLEAR COBALT COMPLEXES of Bohr's frequency rule the allowed electron transitions can be easily calculated with respect to the selection rules summarized in Table III. The most important transitions (in. cm - 1 ) are given in Table IV. and are indicated in Figs. 1 and 2, which show the experimental absorption spectra of the complexes [6]. The figures show that the agreement between the experimental and theoretical results is fairly good. Table II Blu Bzu B2u B3g Blg - 0 . 2 5 9 + 59.168 + 3.940 - 3 . 3 7 3 -1 .561 + 1.881 - 8 . 3 4 4 - 9 . 3 4 3 - 6 . 0 0 4 - 1 . 4 1 7 -6 .021 -7 .211 - 8 . 3 5 7 - 9 . 1 1 0 -11 .374 - 6 . 7 6 6 - 5 . 9 0 5 -12 .264 -11 .919 -11 .927 -14 .136 - 9 . 2 7 5 - 8 . 3 2 8 -14 .718 -14 .754 -14 .107 -12 .622 -12 .160 -14 .883 - 1 4 . 7 9 4 -15 .331 -15 .207 A A . A Ef E" + 1.158 - 1 0 . 5 4 + 49.096 - 2 . 8 8 6 + 2.375 - 5 . 7 7 2 - 0 . 3 1 5 - 6 . 7 2 3 - 5.953 - 9 . 4 7 0 - 8.472 - 8 . 6 7 0 - 9.208 -12 .881 -11 .920 -11 .368 -12 .328 -15 .199 -14 .923 -12 .185 -14 .679 -14 .678 Table III Ai Btu**B3g Biu~*B3g ¿lu~Blg Blg^-B3u Biu-~B2g Ai~E' AÍ~E' AWE" Table IV 2 7 641 27 190 5 938 22 164 12 840 33 588 6 455 26 262 16 653 41 572 8 052 30 797 18 988 47 583 ' 15 088 37 477 25 857 47 616 20 050 43 690 26 803 47 720 21 768 45 150 ;10 V. MARAZ Table V (KA) MO energy (eV) Co o N 3d • 4s 4 p 2 p 2 P 1 b3u - 3 . 3 7 3 22 0 38 10 30 lblu - 5 . 9 0 5 44 ' 1 3 16 36 - 6.004 41 12 7 2 38 2 big - 6 . 0 2 1 40 0 7 24 30 3OI S - 6 . 7 6 6 21 18 7 33 20 -2 b3u - 7 . 2 1 1 34 0 18 34 14 4 blu - 8 . 3 2 8 57 4 • 2 25 12 1 blg - 8 . 3 4 4 59 0 0 41 0 "2 b„„ - 8 . 3 5 7 50 0 10 32 8 2 b3g - 9 . 1 1 0 89 0 5 0 6 - 9 . 2 7 5 62 9 7 12 10 a I„ - 9 . 3 4 3 100 0 0 0 0 • 2 blg - 1 1 . 3 7 4 39 0 0 60 0 3b3u - 1 1 . 9 1 9 15 0 4 58 24 3 blu - 1 1 . 9 2 8 32 • 0 8 45 14 • 5 blu - 1 2 . 1 6 0 23 5 3 51 18 3 big - 1 2 . 2 6 4 14 0 11 60 16 5 alg - 1 2 . 6 2 2 18 7 8 - 48 . 20 462„ - 1 4 . 1 0 7 2 0 10 4 84 3b,g - 1 4 . 1 3 6 0 0 12 0 88 4 big - 1 4 . 7 1 8 19 0 5 8 68 •4 b3u - 1 4 . 7 5 3 20 0 4 11 66 6 blu - 1 4 . 7 9 4 15 9 4 8 64 6 alg - 1 4 . 8 8 3 19 7 2 7 66 7blu - 1 5 . 2 0 7 19 12 0 1 68 1"ig - 1 5 . 3 3 1 12 15 2 3 . 68 In Table V the atomic orbital percentage of occupied and of some empty mo-lecular orbitals are listed, and in Table VI the total gross populations on atoms [7] .-are summarized. Table VII shows the subtotal overlap populations between atoms. According to these results the first and the second bands arise from Co-O bonding orbitals 2b2u, 2b3g, 3e" in both complexes and the remaining two bands .are assigned according to our calculations to the MO's 2b l g , 3b3u, 4a l g , a2, 4e' respectively, which are mainly of Co-0 bonding character and correlate with O orbitals in-origin. The orbital and bond overlap populations are similar in both complexes, but in the case of Kx the orbital population on Co 3d orbital is higher than in the case of K2 and the overlap population between Co atoms in the case •of K1 is less than that of K2. The electron charge densities on Co atoms are also higher in Ki than in K2. According to our calculations^ the resultant electron con-j u r a t i o n s of Co atoms are (3</)5-5 (4.s)0-6 (4p)os for Ki and (3i/)46(4.s)0-8(4/7)0-6 for K2. * * * The author wishes to express his thanks to Dr. F. J. GILDE, Director of the Institute of Theoretical Physics, for helpful discussions 11 V. MARÁZ: M O L E C U L A R ORBITALS O F B I N U C L E A R COBALT COMPLEXES Table V (K,) MO energy (eV) • Co O N 3d 1 4s 4p 2 P 2p 2 a\ - 5 . 7 7 2 16 17 6 41 20' le" - 5 . 9 5 3 43 0 7 24 26 le" • - 5 . 9 5 3 46 0 7 22 24 Se' - 6 . 7 2 3 25 • 0 5 42 18 le' - 6 . 7 2 3 34 0 4 42 • 20 3 a"i - 8 . 4 7 2 52 4 - 1 31 12 9e' -8 .670 48 0 13 30 8 ' 3e' - 8.670 49 0 13 29 10 3e" - 9.208 84 0 1 10 6 8e", - 9.208 82 .0 1 11 6 3 a'x - 9.470 44 26 : 10 6 14 a'i - 1 1 . 2 4 0 0 0 100 0 4e' -11 .368 13 0 4 70 14 10e' -11 .368 13 0 4 71 12 4 a'I -11 .920 12 8 2 64 14 5e' -12 .185 24 0 6 56 ' 14 lie' -12 .185 25 0 6 56 12 4e" -12 .328 20 0 9 53 . 18 9e" -12 .328 19 0 8 55 18 4a[ -12 .881 . 14 • 5 . 8 50 22 6e' -14 .678 22 0 3 10 66 12e' -14 .678 24 0 3 10 62 5e" -14 .679 ' 24 0 4 10 62 \0e" -14 .679 22 0 4 10 64 5a'i -14 .923 4 ' 13 5 14 70 5oi -15 .199 7 16 4 12 62 Table VI Co o N K2 6.673 5.906 4.574 4.684 1.688 and 1.692" 1.689 Table VII C o - C o C o - O C o - N . / * i K, 0.178 0.327. 0.387 0.369 0.277 and Ó.278 0.273 12 V. MARÁZ: MOLECULAR ORBITALS OF BINUCLEAR COBALT COMPLEXES References [1] Pauling, L.: The Nature of the Chemical Bond. Cornell University Press, New York, 1939. [2] Wolfsberg, M., L. Helmholtz: J. Chem. Phys. 20, 837 (1952). [3] Gilde, F.: Dissertation, Szeged, 1958. [4] Landolt—Börnstein: Zahlen werte und Funktionen. Atom und Molekularphysik I (Springer, Berlin, 1954.) [5] Mulliken, R. S.: J. Chem. Phys. 2,792 (1934). [6] Császár, J.: Private communication. [7] Fr aga, S„ G. Malli: Many-Electron Systems: Properties and Interactions W. B. Saunders Company, Philadelphia, London and Toronto, 1968.. ПОЛУЭМПИРИЧЕСКИЕ ВЫЧИСЛЕНИЯ НА ДВУЯДЕРНЫХ КОМПЛЕКСАХ КОБАЛТА МЕТОДОМ МОЛЕКУЛЯРНЫХ ОРБИТ В. Мараз В данной работе рассчитаны энергии, молекулярные орбиты, орбитальные и перекрыт-ные популации и электронные переходы с помощью метода ЛКАО-МО с использованием полуэмпирической формулы Волфсберга — Гельмгольца. 

Semi-empirical molecular-orbital calculations of binuclear cobalt complexes

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Semi-empirical molecular orbital calculations of binuclear cobalt complexes 2.

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