ABSTRACT THE ELECTRONIC AND VIBRATIONAL SPECTRA OF THE HrAMIDO—DECAMMINEDICOBALT(III) ION by Arthur W. Chester Theefiectronic and vibrational spectra of the binuclear gramido-decamminedicobalt(III) ion were determined. The elec- tronic spectrum was analyzed by means of the semiempirical molecular orbital method originated by Wolfsberg and Helmholz and improved by Ballhausen and Gray. The vibrational (infra- red) spectrum was analyzed by means of normal coordinate analysis calculations. The structure of the Efamido-decamminedicobalt(III) ion has been determined by Vannerberg to be bent (C2V symmetry) with a Co-N—Co bond angle of 144°. For the theoretical calcu- lations a linear structure (D4h symmetry) was assumed. The bond lengths were approximated from Vannerberg's data: the cobalt-amido nitrogen bond is 2.2 R; the cobalt-equatorial ammine bond (perpendicular to the major axis) is 2.05 8; the cobalt-axial ammine band (in the major axis) is 1.70 R. The molecular orbital calculations show that the two bands in the electronic spectrum with maxima at 19,740 and 28,010 cm.-1 may be attributed to the electronic transitions (did) xz yz > dx2_y2 and (d ,d ) xz yz > dzz respectively on each cobalt atom. The ordering of the 3d orbital of the cobalt atoms is due to an axially compressed crystal field of C4V symmetry. The very intense band with a maximum at 38,900 cm.-1 is attributed to three L —> M (reduction)charge transfer transitions. Arthur W. Chester Normal coordinate analysis calculations were performed separately for the two infrared regions (NaCl and CsBr). The ligand-vibrations in the NaCl region were similar to those observed in the hexamminecobalt(III) ion, except that three bands were Observed in place of the one rocking vibration in the hexammine. The calculations indicated that these bands were due to the symmetric deformation vibrations of the axial and equatorial ammine groups (1305 and 1334 cm.-1) and the 1 ). A very weak band at NH2 bending vibration (1378 cm.— 1150 cm.m1 is believed to be the NHZ wagging vibration. The frequencies and atomic motions of the skeletal vibra- tions of the E-amido-decamminedicobalt(III) ion were calculated by use of force constants derived from the hexamminecobalt(III) ion. The calculated frequencies were correlated with the observed bands in the CsBr region. That similar force con- stants may be used for the different types of cobalt-nitrogen bonds indicates that the cobalt-amido bridge bond is electron- ically similar to simple cobalt-ammine bonds. The electronic and infrared (NaCl region) spectra of a related ion, the Eramido—chloroaquooctamminedicobalt(III) ion were also determined. The assymmetric band in the electronic Spectrum with a maximum at 20,320 cm."1 was resolved into two bands of equal intensity. The resolved bands are attributed to the transition (d ,d ) ——> d 2 2 on each of the two xz yz x -y cobalt atoms, which are now in different environments. A singlet—triplet transition was also found at 14,200 cm.-1. Arthur W. Chester The relatively high intensity and the assignment of the band are discussed. The infrared spectrum of this compound is similar to that of the E-amido-decamminedicobalt(III) ion and the assignments of the various ligand vibrational bands are discussed. THE ELECTRONIC AND VIBRATIONAL SPECTRA OF THE EfAMIDO-DECAMMINEDICOBALT(III) ION BY . {‘2 Arthur WLVChester A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1966 ACKNOWLEDGMENT The author expresses his gratitude to his wife, Barbara, Whose patience and understanding made this possible; and to Professor Carl H. Brubaker, Jr. for his guidance. Appreciation is also extended to Dr. L. B. Sims for his aid in supplying the vibrational analysis program; Miss Barbara Kennedy, who performed some of the molecular orbital calculations; the Atomic Energy Commission, for financial support. ii TABLE OF CONTENTS Page I. INTRODUCTION . . . . . . . . . . . . . . . . . . 1 II. HISTORICAL . . . . . . . . . . . . . . . . . . . 7 III. THEORETICAL . . . . . . . . . . . . . . . . . . 15 A. Molecular Orbital Theory for Transition Metal Ions .. . . . . . . . . . . . . . . 15 B. Vibrational Analysis (Normal Coordinate Analysis) . . . . . . . . . . . . . . . . 22 C. Electronic Spectra of Cobalt(III) Ammine Complexes . . . . . . . . . . . . . . . . 27 D. Infrared Spectra of Cobalt(III) Ammine Complexes . . . . . . . . . . . . . . . . 31 IV. EXPERIMENTAL . . . . . . . . . . . . . . . . . . 33 Analytical Methods . . . . . . . . . . . . . . 33 Preparation of Compounds . . . . . . . . . . . 34 Preparation of uramido—decamminedi- cobalt(III) Nitrate . . . . . . . . . . . 34 Preparation of Eramido-decamminedi- cobalt(III) Chloride Dihydrate . . . . . 40 Stability of Solutions of the Bridged Complexes . . . . . . . . . . . . . . . . 40 Preparation of Hexamminecobalt(III) Chloride . . . . . . . . . . . . . . . . 40 Spectroscopic Measurements . . . . . . . . . . 40 V. CALCULATIONS . . . . . . . . . . . . . . . . . . 42 A. Molecular Orbital Calculations for the Efamido-decamminedicobalt(III) Ion . . . . 42 Structure . . . . . . . . . . . . . . . . 42 Bonding . . . . . . . . . . . . . . . . . 44 Radial Functions . . . . . . . . . . . . 46 iii TABLE OF CONTENTS (Cont.) Page Group Overlap Integrals . . . . . . . . 46 Evaluation of the Atomic Overlap Integrals 52 Valence State Ionization Energies . . . 53 Energy Calculations . . . . . . . . . . 56 B. Vibrational Analysis Calculations . . . 59 The Cobalt-Ammine (Co-NH3) Systems . . 64 The Amido—Bridge System (Co-NHz-Co) . . 67 The Hexamminecobalt(III) Ion . . . . . 67 The Efamido—decamminedicobalt(III) Ion. 69 VI. RESULTS AND DISCUSSION . . . . . . . . . . . . 75 A. Synthesis . . . . . . . . . . . . . . . 75 B. Electronic Spectra . . . . . . . . . . . 76 C. Molecular Orbital Calculations: Results and Discussion . . . . . . . . . . . . . 82 Results . . . . . . . . . . . . . . . . 82 Bonding . . . . . . . . . . . . . . . . 84 The Electronic Spectrum of the Efamido- decamminedicobalt(III) Ion . . . . . . 87 The Value of q and the §§§§_Treatment . 92 The Spectrum of the Chloroaquo Ion .. . 95 D. Infrared Spectra . . . . . . . . . . . . 97 Infrared Spectra in the NaCl Region . . 97 Far Infrared Spectrum of the Efamido— decamminedicobalt(III) Ion . . . . . . 103 E. Normal Coordinate Analysis Calculations: Results and Discussion . . . . . . . . . 103 iv TABLE OF CONTENTS (Cont.) Page The Cobalt-Ammine and Amido Bridge Systems . . . . . . . . . . . . . . . . 105 The Skeletal Vibrations of the E-amido- decamminedicobalt(III) Ion . . . . . . 113 REFERENCES . . . . . . . . . . . . . . . . . . . . 123 TABLE II. III. IV. VI. VII. VIII. IX. XI. XII. XIII. XIV. XV. XVI. LIST OF TABLES PAGE Orbital transformation scheme for the B“ amido—decamminedicobalt(III) ion in D4h symmetry . . . . . . . . . . . . . . . . . . 47 Radial functions for the atomic orbitals used in the ngcalculations . . . . . . . . . . . 48 Group overlap integrals for the E-amido- decamminedicobalt(III) ion . . . . . . . . . 50 The group overlap integrals for the E—amido- decamminedicobalt(III) ion in terms of atomic overlap integrals . . . . . . . . . . . . . 51 Atomic overlap integrals . . . . . . . . . . 53 VSIE functions for cobalt . . . . . . . . . 55 Coulomb energies used in the Mg calculations 58 Symmetry coordinates for the cobalt-ammine system (C3V symmetry). . . . . . . . . . . . 66 Symmetry coordinates for the amido-bridge system (C2 symmetry). . . . . . . . . . . . 68 v Symmetry coordinates for the u—amido-decam— minedicobalt(III) ion (D4h symmetry) . . . . 72 Electronic spectra of some bridged complexes 77 Parameters for the gaussian analysis of the electronic spectrum of [(NH3)5CONH2CoCl(NH3)5] (N03)5 in water . . . . . . . . . . . . . . 81 Parameters for the gaussian analysis of the electronic Spectrum of [H20(NH3)4CONH2CoCl(NH3)4 ] C14 in 0.1 N HCl . . . . . . . . . . . . . . 81 Energy levels and molecular orbital coeffici- ents for the E;amido—decamminedicobalt(III) ion 83 Infrared Spectra of some bridged cobalt ammine complexes in the NaCl region . . . . . . . . 99 Far infrared Spectrum of Hfamido-decammine- dicobalt(III) nitrate . . . . . . . . . . . 104 vi LIST OF TABLES (Cont.) TABLE XVII. XVIII. XIX. XXII. Force constants for the cobalt—ammine systems . . . . . . . . . . . . . . . . . Force constants for the amido-bridged system Results of the normal coordinate analysis calculations for the cobalt-ammine systems Results of the normal coordinate analysis calculations for the amido-bridge system . Force constants for the skeletal vibrations of the E;amido-decamminedicobalt(III) ion. Results of the normal coordinate analysis calculations for the skeletal vibrations of the Eramido—decamminedicobalt(III) ion.. . vii Page 106 106 107 110 117 118 FIGURE 1. 10. 11. 12. 13. LIST OF FIGURES Page The structure of the E-amido-decamminedi- cobalt(III) ion . . . . . . . . . . . . . . . 5 Qualitative ordering of the one-electron energy levels for tetragonal Co(III) complexes . . . 30 The structure and molecular coordinate system of the Efamido-decamminedicobalt(III) ion for the MQ_calculations . . . . . . . . . . . . . 43 Structure and internal coordinates for the nor— mal coordinate analysis of the cobalt-ammine system . . . . . . . . . . . . . . . . . . . . 65 Structure and internal coordinates for the nor- mal coordinate analysis of the amido—bridge system . . . . . . . . . . . . . . . . . . . . 65 Structure and internal coordinates for the nor— mal coordinate analysis of the Eramido-decammine- dicobalt(III) ion . . . . . . . . . . . . . . 71 The electronic Spectrum of u—amido-decammine- dicobalt(III) nitrate in water . . . . . . . . 79 The electronic spectrum of the Chloroaquo chloride in 0.1N HCl . . . . . . . . . . . . . 80 Proposed molecular orbital energy level diagram for the Eramido-decamminedicobalt(III) ion . . 85 Dependence of coulomb energies of the various orbitals on the charge of the cobalt atoms.. . 93 The infrared Spectra of Efamido—decamminedi- _1 cobalt(III) chloride in the region 650-2000 cm. 98 The infrared spectum of [H20(NH3)4§oNH2CoCl(NH3)4] Cl4°4H20 in the region 650-Z)00 cm. . _. . . . 102 .Schematic diagrams of the A2u and Eu skeletal vibrations of the Eramido-decamminedicobalt(III) ion . . . . . . . . . . . . . . . . . . . . . 120 viii I. INTRODUCTION The phenomenon of a bridging group joining two metal ions occurs widely in the chemistry of transition metal ions. The group which occurs most frequently as a bridge between metal ions is the hydroxyl group. The phenomenon of OH bridge formation is known as "olation"1. Other groups, however, also act as bridges; the amido (NH2-), nitro (N02-), sulfato (8042’), and peroxo (022') groups are some representa- tive examples. Most of the metals in the first transition series form bridged, polynuclear complexes. The most ex- tensively investigated polynuclear complexes have been those of chromium and cobalt. The hexacoordinated complexes of trivalent cobalt played a central role in the development of modern coordina- tion chemistry by A.Werner and have continued in this role up to the present. In the course of his investigations, Werner prepared most of the polynuclear cobalt complexes known today. Werner was able to demonstrate conclusively the octahedral structure of cobalt(III) complexes when he resolved one of these compounds, the tris (di—Erhydroxo- tetramminecobalt(III)) cobalt (III) ion, [Co{(HO)2Co(NH3)4}3]6+ into its optical antipodes3. It was the first completely inorganic compound to be so resolved. In more recent times, bridging groups have played an important role in the study of the kinetics of electron transfer reactions. Taube4t5 and Halpernet7 have shown that 1 the group §_in the reaction + + 2 Co(NH3)5X2+ + Cr2+ + 5H = Co2 + CrX + + 5NH4+ can facilitate electron transfer by formation of a bridge between the cobalt and chromium ions. The formation of bridged intermediates has been shown to be important in other electron—transfer reactions, e.g. the U(IV)—U(VI) exchange and the U(IV)-Tl(III) reactions. Halpern and Orgel9 and Libby10 have proposed mechanisms for these reac— tions. Since there has been much interest in this labora- tory in electron transfer reactions involving bridged inter— mediateslltlz, an investigation of stable bridged complexes seemed in order. Among the most interesting stable bridged complexes are the so-called "Hyperoxo" complexes of cobalt. These compounds were first prOperly characterized by Wernerz, who proposed the currently accepted formulae. Two members of the "Hrperoxo" series are the Erperoxo-decamminedicobalt (III,Iv)([(NH3)5CoOZCo(NH3)5]5U, and Erperoxo-Eramido- octamminedicobalt(III,IV)([(NH3)4CO(NH2,02)Co(NH3)4]4+)ions. These compounds are paramagnetic and contain what are formally trivalent and quadrivalent cobalt atoms. Since quadrivalent cobalt is not known in any other compound, the stability exhibited by these compounds seems unusual. However, electron paramagnetic resonance studies of some of these compounds have demonstrated that the two cobalt atoms are equivalent13'14 thus invalidating the cobalt(IV) assignment. Recently, Schaefer and Marsh15 have Shown by 3 a single-crystal X—ray diffraction study that the oxygen- oxygen distance is more typical of a superoxide ion. This determination agrees with the proposal of Gleu and Rehm16 that the paramagnetism is due to the superoxide ion rather than to the cobalt atoms. The relationship of the peroxo complexes to synthetic reversible oxygen carriers is also of interest. Synthetic oxygen carriers are usually cobalt(II) complexes of Schiff bases or amino-acids which reversibly absorb and release molecular oxygen17. Synthetic oxygen carriers are also formed from other transition metal ions, such as iron(II), nickel(II) and COpper(II), but the largest number are derived from cobalt(II). These compounds are of importance as model compounds for the study of oxygenation mechanisms in natural oxygen carriers such as the hemoglobins and hemocyanins. The oxygenation-deoxygenation process may be illustrated by the cobalt(II)—histidine systemls: CoL2 + O2 = [CoL2]202 (L = histidine) From the formulation of the oxygenated complex, it seems probable that it is a binuclear cOmplex containing an oxygen bridge between the cobalt atoms. Other oxygen carriers are similar. The valence states of the cobalt atoms and the oxygen bridge are not known. It seems probable that these compounds are structurally similar to the Erperoxo-decammine- dicobalt(III,IV) ion (which can be considered as an irrevers- ible oxygen carrier) and thus fall into the realm of bridged complexes. 4 It was initially intended that this investigation be concerned with a theoretical study of the oxygen bridge in the peroxo complexes of cobalt. However, it was found that there was a notable lack of knowledge regarding the electronic structures of "normal" bridged complexes (those which exhibit normal metal ion oxidation states) and the differences be- tween the "normal" complexes and the Esperoxo complexes would be unclear. Such a view was reinforced by the lack of certain knowledge (at the time) of the structures of the peroxo complexes. It was felt, then, that there would be more to gain initially with a theoretical investigation of a model bridged compound containing normal valence states as well as a simple bridging group. The compound chosen for this study was the Eramido- decamminedicobalt(III) ion: [(NH3)5coNHzco(NH3)515+ - This compound is the simplest member of the series of binu— clear ammine complexes of cobalt(III) and corresponds to the octahedral hexamminecobalt(III) ion of the mononuclear cobalt(III) ammine series. This complex was first prepared and thoroughly characterized by Wernerzt19 in 1908. More recently, the structure of the nitrate salt of this ion was determined by Vannerberg20 by X—ray diffraction techniques. The structure is shown in Figure 1. The unit cell is tetra- gonal with 11.68i0.03 8 OJ ll 8.28:0.02 R. 0 ll Figure 1. The structure of the Eramido-decamminedicobalt ionzo. Open circles are NH3 groups, dark circles are co- balt atoms, hatched circle is the NHZ group. (The four NH3 groups perpendicular to the plane are.not Shown.) 6 Since the molecule is bent, it has C2V symmetry. For the theoretical investigation of the electronic and vibrational spectra of this molecule, the simplifying assumption was made that the bridge is linear, i.e. the cobalt-nitrogen-cobalt angle is 180° instead of the re- ported 144°. This approximation has a relatively small effect on calculated electronic energy levels, but has a somewhat larger influence on vibrational frequencies. These effects will be discussed in the body of the thesis. II . HISTORICAL Polynuclear complexes of cobalt were prepared as long ago as 1852. At that time, Fremy21 prepared the diamagnetic Hyperoxodecamminedicobalt(III) ion by oxidation of an aqueous ammonical cobalt(II) solution. Work in the next few decades centered on the preparation of the diamagnetic and paramagnetic Egperoxodicobalt salt522‘27. In the course of those investigations, other bridged products were iso- lated from the oxidized solutions. The products were generally mixtures from which other Hyperoxodicobalt com- plexes could be prepared. The most important of the products were the "Melanochlorid"22‘24, from which various complexes containing three bridges can be obtained, and the I "Fuskosulfat" (now known as Vortmann's Sulfate)21'24'25'27, from which complexes with one or two bridges can be obtained. It was not until the first decade of the 20th century that the nature of these polynuclear complexes was fully understood. At this time Werner published a series of ten papers in which he unambiguously demonstrated the formulae and chemical properties of the above mentioned products as well as many new polynuclear cobalt(III) complexesz'19I28’35° Werner gave complete preparations for both the ”Melano¥ Chlorid"2 and Vortmann's Sulfate33 as well as determining the nature of major constituents of each. He reported the preparation and structural formulae of salts of such ions as di-Erhydroxo-octamminedicobalt(III)32, tri-Erhydroxo- hexamminedicobalt(III)34, g;-amido-Erhydroxo-octamminedicobalt(III)E’3 7 8 Ersulfato-Eramido-octamminedicobalt(III)2 and the Efamido— decamminedicobalt(III)2:19. In addition, he prepared and characterized other triply—bridged, binuclear cobalt com- plexes containing bridging groups such as peroxo, hydroxo, nitro, amido, and acetato2 as well as complexes in which the ammine groups in some of the above ions were replaced by .ethylenediamine groupsz. In the last paper of the seriesz, Werner gave a coherent, if somewhat lengthy, summary of the results which led to his proposed structures. With the exception of the Efperoxodicobalt compounds, relatively few reports concerning bridged complexes have appeared in the literature Since Werner's last paper con- cerning them. Werner3 reported the successful resolution of the "hexol" ion [Co{(OH)2Co(NH3)4g]6+ and of the E“ peroxo-Eramido-tetrakis(ethylenediamine)dicobalt(III,IV) ion35. Meyer, Dirska, and Clemens37 reported the prepara- tion of the selenate salts of some bridged complexes, as well as complexes in which a selenate group acts as the bridge. Very little work has been reported regarding the spectra of "normal" bridged complexes. The first report is that of Shibata38 in 1916 on the visible and ultra- violet Spectrum of the H;amidoagrhydroxo—octamminedicobalt(III) ion. He reported a band at 21,000 cm.-1 and one at 34,000 cm._ . Due to his rather primitive equipment, however, these values give only a qualitative representation of the spectrum. The next report is that of Ohyagi39. He determined the 9 visible and ultra-violet spectra of phosphoric acid solutions of most of the polynuclear cobalt ammine complexes originm ally prepared by Werner. The Spectra were rather crude and are indicative only of the relative band positions and the number of bands. The fact that Ohyagi's Spectra do not agree with the positions of the maxima and, in some cases, the line shapes reported in the present and other investiga— tions, is undoubtedly due to the primativeness of his equip- ment (colorimetric). Inamura and Kondo4° have also reported the spectra of a number of hydroxo-bridged cobalt ammine complexes. More recently, in connection with other investigations, the positions of maxima and molar absorptivities of some bridged cobalt complexes have been reported41‘43. The visible and ultra—violet spectra of the paramagnetic E? peroxo-decamminedicobalt(III,IV) ion have been more ex- tensively investigated39'44‘46. Reports of the infrared spectra of the polynuclear cobalt ammines are even more scarce. Blyholder and Ford47 have reported the far infrared (CsBr region) spectra of a number of dihydroxo-bridged cobalt ammines. They have assigned a strong band at 530 cm._1 to the motion of the cobalt-oxygen four membered ring and a band at about 500 cm.-1 to the cobalt-nitrogen stretching vibration. Vanner— berg and Brosset48 have reported the infrared spectrum of Efperoxo-decamminedicobalt(III,IV) nitrate in the rock-salt -1 . region. They found peaks at 3200 cm. (N-H stretching), 10 1630 cm.-1, 1350 cm.-1, and a double peak with maxima at 820 and 840 cm.-1. Since Werner's work2119I23‘35, little has been re- ported until recently on the reactions of bridged cobalt ammine complexes. Charles and Barnartt45 studied the pro- ducts of the decomposition of the diamagnetic salt Bf peroxo-decamminedicobalt(III) sulfate in aqueous sulfuric acid. They identified four of the products of the decomw 2+. [CO(NH3)6]3+. [CO(NH3)5H20]3+ and position as Co [(NH3)5COOZCO(NH3)5]5+ and proposed a mechanism to account for their formation. Sykes has investigated the oxidation— reduction reactions of the Efperoxogg-amido-octamminedi- cobalt(III,IV) ion with Fe2+49 and of the Efperoxo—decamminem dicobalt(III,IV) ion with Fe2+, 503', N02", 8203:, V(IV) and Sn(II)5°I51 and with iodide ion52. Reisel has investi- gated the role of some bridged cobalt ammines, including the Hrperoxo complexes, in the catalytic decomposition of hydrogen peroxidesza. More recently, Mast and Sykes42:43 have studied the interconversion reactions of binuclear cobalt ammines. They reported both chemical and kinetic evidence for the existence of the diaquo complex [H20(NH3)4CONH2CO(NH3)4OH2]5+ a complex not previously prepared. They also studied the kinetics of some intramolecular substitution reactions in doubly-bridged complexes43. Garbett and Gillard have re— ported some interconversionSof similar complexes with ethylenediamine ligands41 and have assigned optical config~ urations to these complexes53. 11 The structures of three bridged cobalt ammines have been investigated by single crystal X-ray diffraction techniques. Vannerberg and Brosset determined the crystal structure of the nitrate of the Efperoxo-decamminedicobalt (III,IV) ion48. Their determination, based on 234 reflec- tions and a final R_factor of 0.19, indicated that the 02 group lies perpendicular to the Co-Co axis and that the oxygen-oxygen distance is 1.45 R. Schaefer and Marsh15, however, have determined the structure of the sulfate tris(bisulfate) salt of this ion based on 1458 reflections and a final R factor of 0.077. They found that the oxygen bridge structure was very Similar to that of hydrogen peroxide, i.e. not perpendicular to the cobaltwcobalt axis. Each cobalt atom is surrounded by an almost perfect octam hedron of 5 nitrogen atoms and one oxygen atom. Moreover, they found the oxygen-oxygen distance to be 1.31 R, a distance more typical of superoxide than peroxide ion54. Their cobalt—cobalt distance, 4.56 2, compared well with that of Vannerberg and Brosset (4.52 8). Vannerberg also investigated the structure of diag- hydroxo-octamminedicobalt(III) chloride tetrahydrate55 and Eramido-decamminedicobalt(III) nitrate2°. The struc~ ture of the E—dihydroxo complex may be described as two octahedra Sharing one edge, as expected. The cobalt— oxygen bond length is 1.94 R and the cobalt-oxygen-cobalt angle is 110°. The two cobalt atoms and two oxygen atoms lie in a plane which also contains two ammine groups on 12 each cobalt atom. The Co—Co distance is 2.97 A and the oxygen-oxygen distance is 2.49 R. The structure of the Heamido-decamminedicobalt(III) ion was mentioned previously (Introduction) and is shown in Figure 1. From the data given by Vannerberg, a cobalt-cobalt distance of 4.18 R is calculated. Theoretical calculations and discussions of bridged cobalt ammine complexes have been confined to the E-peroxo- dicobalt compounds. Dunitz and Orgel56 assumed the 02 bridge to be linear (D4h molecular symmetry) and calculated the approximate ordering of the molecular orbitals by group-theoretic techniques. They concluded that the un— paired electron occupies an antibonding orbital composed of oxygen 2p orbitals and that the formulation of this ion should then be [(NH3)5CO3+(02_)C03+(NH3)5]5+, i.e. the bridge is a superoxide ion. The ordering of higher lying antibonding orbitals was not determined in this qualitative treatment and spectral transitions can not be assigned. Since the assumption of a linear bridge is a good approxi~ mation to the structure recently determined by Schaefer and Marsh15, more importance will have to be accorded this treatment in the future. Vlfiek57 assumed the oxygen bridge to be perpendicular to the Co-Co axis (D molecular symmetry) and applied 2h group theoretic techniques to the system. He concluded that the unpaired electron occupies a molecular orbital in— volving both oxygen (py) and cobalt (dyz) orbitals. He 13 obtained similar results with the Efperoxofiu—amido—dicobalt system. Vannerberg and Brosset later found a structure similar to VlCek's assumed structure48, but Schaefer and Marsh's recent improvement15 tends to invalidate VlCek's treatment. Ebsworth and Weil have also discussed the electronic structure of the peroxo complexes based on electron para- magnetic resonance spectra14. They concluded that the unpaired electron in the paramagnetic peroxo complexes occupies an antibonding Eforbital extending over both co- balt atoms and the oxygen bridge. Weil and Goodman58 studied the electron paramagnetic resonance Spectrum of Hyperoxo-Eramido-tetrakis(ethylenediamine)dicobalt(III,IV) nitrate in a matrix of Eramido-ppnitro~tetrakis(ethylenedi- amine)dicobalt(III) nitrate. They concluded from the high g_values that the unpaired Spin arises from a hole in an otherwise filled molecular orbital and, from the extent of anisotrOpy in the g_values, that this hole is centered primarily on the cobalt atoms. It will be necessary to reinterpret the e.p.r. results in the light of the structure determined by Schaefer and Marsh15. Goodman, Hecht and Weil have adequately reviewed earlier theoretical work on the peroxo complexes5? There has been no reported theoretical work on the "normal" bridged cobalt ammines. However, other bridged Systems have been treated qualitatively. Dunitz and Orgel56 treated the Eroxodecachlorodiruthenate(IV) ion group- 14 theoretically. Jezowska-Trzebiatowska and Wojciechowski5° have also discussed the molecular orbital theory of a number of oxo-bridged complexes. Two reviews concerning the theory and chemistry of the peroxodicobalt complexes are available in the recent litera- ture59'61. The preparation and properties of all the known polynuclear cobalt ammines are thoroughly summarized in "Gmelins Handbuch der anorganischen Chemie"62. III . THEORETICAL A. Molecular Orbital Theory for Transition Metal Ions Molecular orbital theory was first applied to transi~ tion metal complexes by Wolfsberg and Helmholz63, who treated the tetrahedral oxyanions MnO4—, CrO4- and C104” semiempirically. The Wibeerg—Helmholz treatment was later improved by Ballhausen and Gray64 in their treatment of tetragonal vanadyl complexes. Molecular orbital (Mg) theory was then applied to a variety of complexes55-71. The sub- ject has been discussed in a number of recent books72’74 and some of the methods of calculation employed have been illustrated64'7o'72'74. The Wolfsberg—Helmholz treatment is essentially that Of the Linear Combination of Atomic Orbitals-Molecular Orbital (LCAO-MO) method75. In general, the molecular orbitals are taken as linear combinations of the atomic orbitals of the atoms in the molecule. In the case of transition metal complexes, the bonding and antibonding molecular orbitals (MQ'S) are generally given by: §b(MO) = CIWI + c2¢2 (3A-1a) §'(MO) = CI'll/1 + Cz'wz (3A-1b) where the primes indicate antibonding orbitals and g; and 12 refer to the metal and ligand basis functions (in general the subscript 1 refers to the metal, 2 refers to the ligands). The funztions $1 and $2 are linear combinations of the simple atomic orbitals O . and O .: 11 2]. 15 16 "(Z/1 = Z ai3 m.x.2 (SB-1) j=1 l 1 Where mi is the mass associated with the displacement co- ordinate xi and Xi is the time derivative of xi: — —- — _ 23 ii = dxi/dt (3B-1a) In treating molecular vibrations, it is more convenient to Speak of internal coordinates, such as bond stretching or angle deformation coordinates. The internal coordinates Rk may be expressed as linear combinations of the cartesian displacement coordinates xi: 3N Rk = .2 Bki xi (k = 1,2,...,3N - 6) (3B—2) 1:1 The sum over k_runs to 3N_- 6 because it can be shown‘38"90 that any molecule will have 3E.’ 6 unique vibrations when translational and rotational movements are disregarded. Equa- tion (2) may be expressed in matrix notation as: B=_B_x (BB—2a) where R_and X are the column matrices of the internal coordinates and cartesian displacement coordinates, respec- tively. By defining a set of quantities le as 3N le = iEl Bki Bli/mi (k, l = 1,2,...,3N - 6),(3B-3) it has been shown86 that the kinetic energy of the molecule can be expressed in terms of the internal coordinate velo-, cities R . as ki -1 2T = 33.9 (33-4) luv. -1 . where g_ is the inverse of the matrix g, which has the elements given in equation (3); E_is the column matrix of the 24 internal.coordinate velocities and 3' is its transpose (in general, the matrix 2: is the transpose of A). ' It can.also be shown88 that the potential energy, V, may be expressed in a similar fashion: W = B' E B (BB-5) where gzis the matrix of the force constants connecting the internal coordinates Rk' The normal coordinates Qk (k_= 1,2,...,3N) are defined as linear combinations of the mass—weighted Cartesian co— ordinates qi = m. x. as: N Q. = z 1.. q. (j = 1,2,...,3n) (SB-6) such that the kinetic and potential energies have the form: 3N 3N 2T = Z 0.2 2v = Z A. Q.2 (SB-7) o 0 _ l 1 1:1 1-1 where the Ai are constants, i.e. the potential energy has no cross terms. If the equations (7) are combined with LaGrange equations of motion, given by: d/dt(OT/Oqi) + OV/Oqi = o (i = 1,2,...,3N) (BB-8) then the equations of motion of the system are given by Qi + Ai Oi = 0 (33—9) Equation (9) has the solutions: Qi = Q? sin(J xi t + Oi) (3B-9a) where Qg-and Oi are the amplitude and phase constants re- spectively, and Qi is normal coordinate position at time E. The frequency Vi of the iFh normal vibration is related to liby 25 v. = (1/2wchfii cm.-1 i (3B-9b) Normal coordinate analysis finds the frequencies of vibration, vi, and the normal coordinates Qi associated with these frequencies by the use of matrix algebra. The trans— formation L, defined by -1 R = L_Q_or Q_= L '3 (BB—10) is sought such that the kinetic and potential energy matrices given by equations (4) and (5) are diagonalized: -1 -1 2T = 3' B = Q' L' L Q. = B' B. 9'. (BB-11a) IO [0 2v B‘ EB = 2' L' EBB RAB (BB-11b) In (11a) and (11b), §_is the unit matrix and.éris a diagonal matrix with the elementsJ\.ii - Ai. From (11a) and (11b), it can be seen that L' Eli =.I_L and L.‘ G-1 p = E (3B-12) Solving for L] in the second equation in (12) (fl = L. g) and substituting the result in the first equation, the vibra- tional secular equation is obtained: SEL= LA- (313-13) The values of the Ai can then be obtained by solving the secular determinant: = 0 (BB-14) ) [SE - Em From the values of Ai, the transformation matrix L_(or L71 from equation (10) may be determined. The rows of the matrix L. give the normal coordinate Qi in terms of an unnormaiized linear combination of the internal coordinates Rk' 26 The secular-determinant (14) may be considerably'sim- plified by the introduction of the symmetry properties of the molecule. The internal coordinates, R can be trans- kl formed into symmetry coordinates, Sk' by use of an orthog- onal matrix g: Im ll 23. (SB—15) Equations (10) are then replaced by: s-HL9=LS Q (BB-16> 2:2-1 2’1 BB=L;1§ Where L = U L (3B-16a) —S —— The §_and E matrices may then be ”symmetrized", or reduced to block diagonal form, by use of the orthogonal transformations 6., = H S H (BB-17a) ES = H E II.‘ (313-171.) (since g;_- gfl for an orthogonal matrix). The vibrational secular equation (13) then becomes a. E. L. = A. A- (38-18) and the secular determinant (14) is then [gs = 0 . (3B-19) HG Jo l [—5 If the proper matrix has been used, the secular determinant (19) will.be in block diagonal form, resulting in consider- able simplification in finding the solutions Ai 27 C. Electronic-Spectra.of Cobalt(III) Ammine Complexes The electronic spectra of cobalt(III) ammine complexes have been examined by many workers (for instance, Linhard and Weigel91I9a, and have been treated theoretically by both crystal field theory93r97 and molecular orbital theory 8°I93'98'99. The Spectra of Co(III) ammines are generally characterized by two weakly to moderately intense bands (§_j,102) in the visible and near-ultraviolet spectral regions which may be characterized as d-—> d transitions on the basis of their intensities. Crystal field theory (GET), in which the ligands act only as point charges or point dipoles, has been applied more successfully than Mg theory. The parent member of the cobalt(III) ammine series is the octahedral hexammine- cobalt(III) ion. Substituted Co(III) ammines are considered to have the basic octahedral structures with relatively small tetragonal or trigonal perturbations, so that the spectra may be qualitatively understood with reference to an octahedral structure. According to GET, the five degenerate g_orbitals are Split under the influence of an octahedral field into a lower tZg (dxy’ dxz’ dyz) and an upper eg (dX2_y2 and dz?) level. The ground state of the Co(III) ion in a strong octa- hedral crystal field is tgg , of symmetry 1Alg. The first excited state results from the a closed Shell configuration 28 promotion of an electron from the t2g level to the eg level, 5 . . . . 5 . . gIVIng a configuration of t2geg' The configuration t2g eg gives rise to two triply-degenerate singlet states, 1T1g and 1T29 and two triplet states, 3T1g and 3T The energy 29 separation of the lTlg and the 1T2g states is due to cor— relative interactions between the electrons, whose roles have been subordinated by the crystal forces96. The two bands observed may then be assigned to the transitions 1A1g 1g and 1Alg-——> 1ng, and the energies of these tran» Sitions are given by .__> 1T ) - E(1A -35 F + 10Dq V II 1 E(T 4 1g 1g E(2T ) — E(1A ) 16 F2 - 115 F4 + lonq lg 19 where F2 and F4 are the Condon-Shortley interelectronic rem pulsion integralsl°° and 10Dq is the energy separation be-- tween the t and e levels. 29 g Transitions from the ground state to the triplet levels 3T1g and 3T have been observed92'101 in the nearminfrared 29 region. Since these transitions are spin-forbidden, their intensities are very low (5 3.1), although surprisingly high intensities have been found for some bromo- and iodo-sub— stituted Co(III) amminesgz. The energies of the two singlet -? triplet bands are given by E(3T1g) - E(1Alg) = - 105E4 + 10Dq ) = 8F — 24F + 10Dq. 2 4 29 When the symmetry of the octahedral Co(III) ammine com- plexes is lowered by substitution of other ligands, the degenerate t2g and eg levels are split to give lower orbital degeneracies. Of particular interest are complexes of tetragonal symmetry such as the halopentammines (C or 4v) the trangfdihalotetrammines (D4h). If the notation of the point group C4V is used for either case, the t29 level splits into a doubly degenerate e level (dXZ and dyz) and a non-degenerate b2 level (dxy), and the eg level splits into two non-degenerate levels, a1(d22) and b1(dX2_y2). The qualitative ordering of these one-electron levels in the case of axial elongation is Shown according to the predictions of ggg_in Figure 2(a) and according to the pre» dictions of Mg_theory in Figure 2(b). The two theories differ in the ordering of the e and b levels, in that Mg_ 2 . theory takes metal-ligand.flfbonding into account. Figure 2(c) Shows the qualitative ordering of the one-electron levels in the case of axial compression predicted by M9 or EFT. The ground state of tetragonal Co(III) complexes in any of the three cases shown in Figure 2 is e4 b3. The prOm motion of electrons from the filled e and b2 levels to the unfilled a1 and b1 levels results in the observed spectra97. Many tetragonal cobalt(III) complexes exhibit Splitting of the band corresponding to the 1A1 -—> 1T1g band of the octahedral hexammine and it is predicted on the basis of ——> 1T band should 19 29 also be split, although this phenomenon has not yet been diagrams such as Figure 2 that the 1A 30 b1 ‘ dxz-y2 b1 a1 a1 E dzz a1 b1 b2 3 dXy e e e E dxz’dyz b2 b2 (a) (b) (C) Figure 2. Qualitative ordering of the one-electron energy levels for tetragonal Co(III) complexes. (a) Q§T_prediction for axial elongation (without 1- bonding) (b) Mg_theory predictions for axial elongation (with 17b0nding) (c) prediction for axial compression (Mg_theory or CFT). The notation is defined in (a). 31 observed. More Specific information regarding the various approaches has been given by Wentworth and Piper97'99. D. Infrared Spectra of Cobalt(III) Ammine Complexes Infrared Spectra of a large number of Co(III) ammine complexes have been published47'102“105 and theoretical calculations have been performed for the Co-NHé system1°5tl°7 and the octahedral Co(NH3)g+ system1°8r1°9. The spectra of Co(III) ammine complexes in the region above 650 cm._1 (NaCl region) are characterized by the vibram tion of the NH3 group. The four bands (or sets of bands) that appear in the NaCl region have been assigned on the basis of a vibrational analysis of the Co-NH3 system1°6r1@7. The N-H stretching vibration is observed in the region of 3200 cm._1. The three other bands at about 1600, 1300, and 800 cm.”1 are assigned as the NH3 degenerate deformation, NH3 symmetric deformation and the NH3 rocking vibrational frequencies, respectively. It has been found that the three NH3 deformation frequencies are affected by the nature of the anion present1°2, and the changes have been ascribed to hydrogen bonding between the ammine hydrogens and the anions. The spectra of Co(III) ammine complexes in the region below 650 cm.-1 (CsBr region) are characterized by skeletal vibrations. Generally, spectra of Co(III) ammines in the CsBr region show a set of three weak bands between 450 and 550 cm.-1 and a strong, broad band between 300 and 350 cm._1. In case of the octahedral hexamminecobalt(III) ion, there 32 are six skeletal vibrations, of which only two are infrared active: the assymmetric Co—N stretching vibration and the N-CorN angle of deformation vibration, both of which trans- form as the T1u representation of the point group Oh' Block1°8 assumed that the NHg groups are in weak libra~ tion about the Co-N axis and calculated the vibrational frequencies for the Co(NH3)g+ system. He concluded that the Co—N stretching vibrational frequency should be in the region of 500 cm.-1, but did not calculate the angle deforman tion vibrational frequency. Shimanouchi and Nakagawa“):9 treated only the CoN6 octahedron and concluded that the stretching vibrational frequency should be at 464 cm.“1 and the angle deformation vibrational frequency at 329 cm.m1. Similar results were obtained for substituted Co(III) ammines. From the above theoretical treatmentsl°8'1°9, it is pOSe sible to tentatively assign the observed bands of Co(III) ammines in the CsBr region. The set of three weak bands between 450 and 550 cm.-1 is due primarily to the Co~N stretching vibration and the strong band between 306 and 350 cm.“1 is due primarily to the angle deformation vibram tion. Since both vibrational modes transform as Tlu’ there is considerable mixing, so that neither vibration is pure stretching or angle deformation. The splitting of the stretching vibration into three bands remains unexplained, although Nakamotoll° has attributed the phenomenon to the influence of the octahedral crystal field. IV . EXPERIMENTAL Analytical Methods Cobalt Analysis - Cobalt was determined Spectrophotometrically as the blue tetrathiocyanatocobaltate(II) complex in 50% by volume aCetone-water solution. The cobalt(III) ammine complex was decomposed to give cobalt(II) sulfate by treatment of a 10—12 mg. sample with 5-7 drops of concentrated sulfuric acid followed by gently heating the sample to dryness. The cobalt(II) sulfate was dissolved in a few ml. of water by gentle heating and the solution was transferred to a 100 ml. volumetric flask. The cobalt(II) solution was then treated with 5 ml. satur— ated ammonium thiocyanate solution, and 50 ml. acetone, and then the flask was filled to the mark with water. The ab~ sorbance of the solution at 620 mu was determined with a Beckman DU Spectrophotometer. The molar absorptivity of the tetrathiocyanatocobaltate (II) complex at 620 mu was determined by use of a cobalt(II) sulfate solution which had been standardized by the method of Laitinen and Burdettlll. The solution of the thiocyanate complex obeyed Beer's Law at 620 mu and had a molar absorp- tivity of 1817 i 14. The 1 cm. silica cells used in the determination were recalibrated against each other periodic- ally by use of the standard cobalt(II) sulfate solution. 33 34 Nitrogen and Hydrogen Analyses - Nitrogen and hydrogen analyses were performed by the Spang Microanalytical Labora— tory, Ann Arbor, Michigan. Water Analyses - Water of hydration was determined by drying in vacuo for 6 hours over P205. Preparation of Compounds Preparation of Eramido-decamminedicobalt(III) nitrate m The preparation of the Eramido—decamminedicobalt(III) nitrate generally followed the procedures given by Werner2r19. A less detailed procedure has also been given by Vannerberg2§ The series of reactions used in the synthesis are as follows; 2+ + 4Co(H20)6 + 18NH3 + 02(g) + 5802' + 2H "—> [(NH3)4CO(NH2vSO4)C0(NH3)4)]2(504)3 + 2H20 (1) [(NH3)4CO(NH2ISO4)CO(NH3)4]2(504)3 + 6NO3- '——> 2[(NH3)4CO(NH2ISO4)CO(NH3)4](N03)3(I) + 350:” (2) [(NH3)4CO(NH2,SO4)CO(NH3)4](N03)3 + 5C1” + H20 -—> [HZO(NH3)4CONH2COC1(NH3)4]Cl4(II) + 302‘ + 3N0; (3) [H20(NH3)4CONH2COC1(NH3)4]Cl4 + 4N0; ——> [NO3(NH3)4CONH2CoCl(NH3)4](N03)3(III) + 4C1” (4) [NO3(NH3)4CONH2CoCl(NH3)4](N03)3 + 2NH3 ——> -——> [(NH3)5CoNH2CO(NH3)5](N03)4C1(IV) (5) [(NH3)5CoNH2Co(NH3)5](N03)5Cl + N03- ——> [(NH3)5CoNH2Co(NH3)5](N03)5(V) + Cl" (6) 35 Because the synthesis is a very difficult process, the complete procedure is given below. (a) Preparation of Beamido—u-sulfato-octamminedicobalt (III) nitrate trihydrate (compound I, reactions 1 and 2) - One hundred grams of Co(NO§)2°6HZO was dissolved in 450 ml. water in a 2000 ml. filter flask and 650 ml. concentrated ammonia was added while the flask was swirled. The solution was oxidized by bubbling air through a 10 mm. glass tube very slowly for 8 hours. The oxidation resulted in a dark brown solution which was allowed to stand overnight (about 14 hours) at room temperature. The solu~ tion was cooled in an ice bath and acidified by the drOpwise addition of a mixture of 300 ml. concentrated sulfuric acid and 400 ml. water over a periOd of 4 hours (the ice cooling was maintained throughout this period). When the acidifica- tion was complete, the solution was cooled at about —10°C. (in a refrigerator freezing compartment) in a stoppered flask for about 5 hours. The cooled solution was filtered through a medium fritted funnel. The solid obtained was washed with two 100 ml. portions of ethanol and 50 ml. of ether and then was air-dried. The yield of the red solid (crude Vortmann's Sulfate) was 54 g. The crude Vortmann's Sulfate (54 g.) was stirred thor- oughly with 75 ml. concentrated nitric acid and allowed to stand for about 30 minutes. Water (110 ml.) was slowly stirred in and the mixture was filtered through a medium 36 fritted funnel. The solid obtained was washed with four 100' ml. portions of water, two 50 ml. portions of ethanol, 50 ml. of ether, and was then air-dried. The red solid was grude Eramido-Ersulfato-octamminedicobalt(III) nitrate and the yield was 20 g. A pure sample of u—amidoaursulfato-octamminedicobalt(III) nitrate trihydrate, [(NH3)4Co(NH2,SO4)Co(NH3)4](NO.)5-3H20 compound I, was prepared by washing the crude product with large amounts of water (about 1 liter in 10 to 15 portions), though the yield was considerably reduced because of the compound's solubility in water. Anal. Calc'd.: Co, 19.4. Found: Co, 19.3. The compound may also be recrystallized from dilute nitric acid. The infrared spectrum of compound I in the region of sulfate absorption (900-1200 cm._1) agreed with that given by Nakamoto, 32.313112. The four sulfate bands were found at 998, 1062, 1109, and 1161 cm.‘1. In an attempt to determine the major product of the oxidation, (as well as to identify the major impurity in the above-mentioned compounds) a portion of the filtrate ob— tained in the separation of the crude Vortmann's Sulfate was treated with excess sulfuric acid and cooled at —10°C. An orange-yellow crystalline solid separated and was filtered, washed with ethanol, and dried. The compound gave a White precipitate with Ba2+ and had absorption peaks at 340 and 478 mu. The absorptions correspond to the hexamminecobalt(III) 37 Sulfate, which.could.then be regarded as the major product of the oxidation-as.well as the major impurity in the crude u:amido-Ersulfato-octamminedicobalt(III) nitrate. It is also probable that the hexammine was the major impurity in the compounds subsequently obtained in the synthesis. (b) Preparation of uramido—6-chloro-6'-aquo-2,2',3,3', 4,4',5,5'-octamminedicobalt(III) Chloride tetram hydrate (compound II, reaction 3) - (This compound and its complex ion will be referred to henceforth as the "Chloroaquo chloride" and the "Chloroaquo ion", respectively.) The crude Eramido-uesulfato-octamminedicobalt(III) nitrate (20 g.) was treated with 280 ml. concentrated hydrochloric acid in a 500 ml. erlenmeyer flask and allowed to stand at room temperature for about 25 hours. The mixture, which was blue due to some formation of CoClZ- ion, was filtered through a medium fritted funnel. The solid was waShed thoroughly with ethanol to remove all traces of Co(II). It was then washed with about 50 ml. ether and air-dried. The yield was 15.6 g. of the EEEQE.chloroaquo chloride. A sample of the compound was purified as follows: 5 g. of the crude product was dissolved in warm (45-50°C.) water, and the solution was filtered. The resulting dark solution was then cooled in a 5°C. refrigerator for a few hours and filtered. Dark purple-red crystals of cOmpound II were ob- tained, yield 2.2 g. 5221: Calc'd. for [H20(NH3)4CONH2COC1 (NH3)4]C14°4H20: Co, 21.9; N, 23.45; H, 6.75; H20, 13.40. Found: Co, 22.5, N, 23.73; H, 6.84; H20, 13.36.; 38 (C) Preparation of uramido-6-chloro-6'—nitrato-2,2LL 3,3',4,4',5,5'-octamminedicobalt(III)_nitrate (compound III, reaction 4)_- (This compound and its complex ion will be referred to henceforth as the "chloronitrato nitrate" and the “chloronitrato ion", re- spectively.) The crude Chloroaquo chloride (compound II, 12.5 g.) was treated with 185 ml. concentrated nitric acid and the mixture was stirred thoroughly and warmed slightly on a steam bath. After the mixture had cooled, it was filtered through a medium fritted funnel. The solid obtained 'was dried by sucking air through the filter, and was then washed with 50 ml. ethanol and 20 ml. ether (It is particu— larly important that all_the HNO3 be removed from the solid before adding ethanol, since cobalt(III) ammines apparently catalyze the oxidation of ethanol by HNO3 in the absence of water. If the HN03 is not completely removed, a violent reaction ensues. It is also necessary to add about 50 ml. of water to the filtrate in the filter flask to prevent the occurrence of this reaction in the filtrate.) Airedrying gave 11.5 g. of the crude chloronitrato nitrate (compound III). Attempts to purify this compound by recrystallization from water or dilute nitric acid were unsuccessful. When a fresh aqueous solution of the crude product was treated with Ag+, a white precipitate was observed only after heating, and thus the presence of coordinated chloride was demonstrated. 39 (d) Preparation of E-amido-decamminedicobalt(III) chloride tetranitrate (pompound IV, reaction 5). — Two 5 g. portions of the crude chloronitrato nitrate (Com- pound III) were each treated with 750 ml. liquid ammonia in 1 liter Dewar flasks. The flasks were stoppered and the solutions allowed to stand for 2 days (ammonia was added to maintain the volume of the solutions). The stOppers were then removed and the ammonia was allowed to evaporate slowly (about 2 days). The last traces of ammonia were removed by heating the residues with an infrared lamp. The solid that remained was transferred to a beaker and treated with about 70 ml. water. The mixture was then warmed gently for 5 minutes on a steam bath and filtered, while still warm, through a medium fritted filter. The reddish-pink solid was washed with ethanol and a little ether, and air-dried. Yield, 4.9 g. of crude Efamido-decam- minedicobalt(III) chloride tetranitrate (compound IV). (e) Preparation of_E-amido-decamminedicobalt(III) nitratey(compound V, reaction §)_- One and three tenths grams of the Eramido-decamminedicobalt(III) Chloride tetranitrate (compound IV) were dissolved in 200 ml. of water containing 5 ml. of 3N nitric acid by heating on a steam bath. After the hot solution was filtered, it was allowed to cool slowly to room temperature. Deep red crystals of [(NH§)5CONH2CO(NH3)5](N03)5 (compound V) were obtained, yield 0.5 g. Anal. Calc'd.: Co, 19.2. Found: CO, 19.2, 19.0. 40 Preparation of u—amido—decamminedicobalt(III) chloride di— hydrate — The chloride tetranitrate (compound IV) was con- verted to the chloride by saturating an aqueous solution with ammonium chloride. The solid filtered from the solu- tion was recrystallized twice from 5% (by volume) hydro- chloric acid. The final product consisted of very fine red needles. Aril- Calc'd. for [(NH3)5CONH2CO(NH3)5]C15°2H20: Co, 22.8. Found: Co, 22.6, 23.1. Stability of Solutions of the Bridged Complexes - Aqueous solutions of all the above compounds were found to decompose within 24 hours, depositing a yellow-brown solid. The Chloroaquo chloride displayed the lowest stability, generally decomposing within 1 hour or less. It was found, however, that dilute acid solutions of these complexes were stable for at least a month, if not more. It is therefore probable that the decomposition in aqueous solution is due to attack of the amido bridge, since the bridge is undoubtedly pro- tonated in acid sOlution. Preparation of Hexamminecobalt(III) chloride - This compound was prepared by Walton's procedure113. Large orange crystals. Anal. Calc'd. for Co(NH3)6C13: Co, 22.00 Foundzu Co, 22.0. Spectroscopic Measurements Absorption Spectra of solutions in the near infrared, visible, and ultra-violet regions (200-1000 mu) were deter- mined on a Cary 14 Spectrophotometer with 1 cm. silica cells. 41 Because of the instabilities of the bridged complexes in aqueous solution, all spectra were determined from freshly prepared solutions. Infrared absorption Spectra in the sodium chloride region (650-5000 cm.-1) were determined in potassium bromide pelkats or Nujol mulls on a Unicam SP-200 Infrared Spectro- photometer. Spectra in the cesium bromide region (250- 650 cm.-1) were determined in Nujol mulls on a Perkin-Elmer 301 Spectrophotometer. V . CALCULATIONS A. Molecular Orbital Calculations for the uramido—decammine; dicobalt(III)_ion. Structure - A "linear", D4h structure was assumed for the E? amido-decamminedicobalt(III) ion (referred to henceforth as the "decammine ion") for the purposes of the M9_calculations, shown in Figure 3. The bond lengths were approximated from Vannerberg's struCtural determination2° (Figure 1) and are shown in Figure 3. The hydrogen atoms were neglected; the ammine groups and the amido group: were treated as nitrogen atoms and a negative nitrogen ion, respectively. As can be seen in Figure 3, there are three types of equivalent nitro- gen atoms in the decammine ion: eight equatorial nitrogen atoms (Ne), two axial nitrogen atoms (Na), and the bridging nitrogen ion (Nb). The molecular coordinate system is also Shown in Figure 3. The z axis was taken as the fourfold axis and the x and y axes were taken to be parallel to the Co-Ne bonds. The origin was placed at the bridging nitrogen. The linear structure was assumed for the decammine ion primarily to take advantage of the higher symmetry (relative to Vannerberg's bent structure of sz symmetry) in factoring the secular determinant in the energy calculation (equation (3A-11). In View of the limitations of the Wolfsberg-Helmholz Agznethod discussed in Section IIIA, the relative ordering of 43 .QZ pm we cflmfluo 0:9 .%Hw>fluummmmu mcflmpflun cam .HMHHOpmsvm .HMme uswmwummu meoum cmmoupflc may so.m Cam .w..m.mumHHOmQ5m 0:9 .msOHumasuamu mm.w£u How GOH AHHHVDHMQOOHUOGHEEMOOUIOUHEmhm TAD mo Emumhm mpmsflpuooo HMDHQHO HMHDOOHOE Cam mwocmvmflp .mnsuOsHum 039 .m musmflm 02 Oz 0 OZ Z no no no we we / 9... mo Nb 0 Z so 2 Ho mm0.N m 2 oz 44 the one—electron energy levels should not be affected by the assumption of a structure of higher symmetry. The degenerate levels which occur because of the higher symmetry of the linear structure would be Split if the symmetry were lowered to C2v’ but this splitting is probably negligible in comparison with other energy differences. In addition, the structure of the decammine ion in solution might approximate the assumed linear structure. In order to predict correctly the polari- zations of the electronic transitions in crystals containing the decammine ion, however, it would be necessary to use the symmetry group C2v' Bonding - In the Mg calculations for the decammine ion, only .g- bonding was considered for the Co-Ne and Co-Na bonds° The equatorial and axial g7 bonds are shown in Figure 3 along with the numbering system used in the calculation of the orbital transformations. In the case of the bridge system (Col-Nb-Coz) both 1% and gr bonds were considered. The orientation of the bridge E? and g5 bonds are Shown in Figure 3 (£2, Ex and fly). The equatorial and axial nitrogen gforbitals were as- sumed to be hybrid orbitals of the form: ¢(26) - (sin 9)¢(2s) i (cos 9)¢(2p or 3d) (SA-1) The degree of hybridization was estimated after the man- ner of Ballhausen and Gray64, by minimizing the quantity VSIE (9)/8(9), where SL6) is the overlap between the hybrid orbital and the appropriate cobalt orbital. VSIE (9) is the 45 valence state ionization energy for different amounts of mixing Qflcalculated from the relationship: H(20) = (sin2 9) H(2s) + (cos2 6) H(2p) (SA-2) where H(ZO), H(ZS), and H(ZE) are the coulomb integrals (the negative of the VSIE) for the hybrid orbital, the pure 2s orbital and the pure 2p orbital, respectively. The minimiza- tion of VSIE(6)/S(G) gave values of 9e = 0.243 and 9a 0.314 radians for the equatorial and axial nitrogen gforbitals, respectively. These values correspond to 5.9% and 9.5% 23- character for the equatorial and axial hybrid gforbitals, respectively. The gforbitals on the bridging nitrogen ion (g2) were assumed to be pure 25 and 2pz atomic orbitals. The 25 orbital was not included in the calculations for reasons to be dis- cussed later. The lforbitals (Ex and fly) on Nb were taken as pure 2pX and 2py atomic orbitals. The ligand group orbitals (linear combinations of the atomic or hybrid orbitals of the individual ligand atoms) were determined by use of standard group theoretical techni- ques72'74'32. The cobalt 3d, 45, and 4p atomic orbitals were used in the calculation. The 3d22 and 4s atomic orbitals were as— sumed to mix according to equation (1) with Q_=‘114 radians (50% 4s, 50% 3d22)' The cobalt group orbitals (linear combinations of the atomic orbitals of the two cobalt atoms) were taken as sum and difference combinations of the atomic 46 orbitals on the two cobalt centers. Thus the cobalt group orbitals had forms such as (3d; 2 1 2 i 3dxy) and 4pX i 4px), Y where the superscript indicates the cobalt atom to which the atomic orbitals belong. Metal—metal overlap (which would be extremely small for the decammine ion, Since the Co-Co distance is 4.4 A in the linear structure) was neglected in the normalization of the cobalt group orbitals. The orbital transformation scheme for the decammine ion is shown in Table I. Radial Functions - The cobalt 3d, 45, and 4p functions were taken from the data of Richardson, gt, al.114'115, by use of the data for a charge of +1 on the cobalt atom (since the cobalt atoms were assumed to have a charge). The radial functions for the nitrogen 25 and 2p orbitals were calculated from the data of Hartree116. The radial functions used in the calculations are summarized in Table II, where the indi- vidual terms have the form of a Slater-type orbital (SEQ): n-1 —ur c» u) = N r e (SA—3) n( where n'is the principle quantum number, u.i5 the "Slater exponent" and N_is the normalization constant, given by 2n—1 , 1 N = [(23) /(2n>.1 (2 (SA-3a) Group Overlap Integrals - Equations relating the group over- . , . . . . lap integrals (Gi' 5) to Simple diatomic overlap integrals (S..'5) were determined by the methods that have been out- _£l__ lined in detail by Bedon, et._al.7°, Ballhausen117 and 47 Table I. Orbital transformation scheme for the Efamido- decamminedicobalt(III) ion in D symmetry. 4h Repre- senta— Cobalt Orbitals Ligand Orbitals tion a 1 (4 1 — 4 2) 1 (O + O ) 1g J2' pz pz J2' 9 1° %{(451+3d;2)+(452+3d:2)] 3%(01+02+03+04+05+06+07+08) l. 1_ 1 2_ 2 2[(4s 3d22)+(4s 3d22)] . . . . blg J-Z-(3dX2-y2+3d XZ’YZ) 3.8—)01-02+O3-O4+O5_06+G7-O8) b 1(3d1 + 3d2 ) 2g 72' xy xy ° ' ° ' ' 1 4 1 2 1 eg 751 PX - 4px) '§(01‘03+05‘07) 1 4 1 4 2 1*. J2( Py - PX) 2(02‘04+06'07) 1(3611 + 3d2 ) 72' xz xz ° ° ’ ' 1(3d1 + 332 ) 72' yz yz ' ° ' a 1(4 1 + 4 2) 0 2n J2- pz pz 2 1 4 1 1 4 2 3d2 1 §T( S +3dzz)‘( S + z2)] 75(09 ‘ O10) 1- 4 1 3d1 4 2 3d2 1 - - ) 2[( S ' zz)-( S - z2)] J§101+02+03+04'05 06 07-08 b 1(3d1 - 3d2 ) 1u J2' xy xy ' ' ' ° ' 1 2n 72*3d§2-y2‘3d§2_y2) (Ox-02+Ga-O4-Os+06-o7+o.) Ede 1 1 en 35(4P; + 4P:) '§(01‘03‘05+07) 1- 1 J514P; + 4P?) 5(02‘04‘06+08) 1 1 _ 2 1 3d1 - 3d2 J2< yz yz) WY 48 Table II. Radial functions fo the atomic orbitals used in the Mg calculations . Cobalt- R(3d) = 0.568¢3(5.55) + 0.606¢3(2.1O) R(4s) = -0.02078¢1(26.375) + 0.06920¢2(10.175) —0.1697¢3(4.69) + 1.0118®4(1.45) R(4p) = 0.01091¢2(11.05) - 0.03681¢3(4.385) + 1.00061¢4(O.83) Equatorial and axial nitrogen — R(25) = ¢2(2.25) R(2p) 02(1.77) Bridginqinitrogen- R(25) = 02(2.16) R(2p) ¢2(1.42) ¢n(u) = N tn"1 e'”I . 49 Ballhausen and Graylls. The expressions were derived by substituting the relevant cobalt and ligand group orbitals in the equation: Gij = f wi wj dT (SA-4) Equation (4) was then expanded. The approximation of zero overlap between orbitals on atoms not directly bonded to each other was used. This principle may be demonstrated for the . 1 1 2 case of the overlap between the eg orbitals J2(4px 4px) and %(01—03+05-O7) by the following transformations: G[eg(O)] =fJ-%(4p;-4p:)%(01—O3+O5-O7)dT (5A—5a) = 5%Eif4p;<01‘03)dI'f4P:(O5-O7)dT] (5A-5b) = 7,13 f4pO(01-03)dT (5A-5c) = Jg-f(4po)(2o) d; (SA-5d) = J2[S(2o,4po)] (SA—5e) where 20 and 4pO represent the hybrid ligand atomic orbital and the cobalt 4p orbital, respectively. The values of the group overlap integrals are given in Table III, in which the Mgfs are defined. Interactions not listed in Table III were assumed to have zero overlap (e.g. the overlap of the eg orbitals J%(3d;z + 3d;z) and %(01-O3+05-O7) was assumed to be zero). The relationships between the G..'s and S..'S are listed in Table IV. _£l .451 50 Table III. Group overla integrals for the uramido— —decammine- ‘ dicobalt(III ion. Molecular Orbital Cobalt Orbital Ligand Orbital Gij 1 Italgwm The; - 43,) 7240.451.) 0.090 §[alg(02)] 11(451+3d12)+(452+3d22)]f%’(09+010) 0.177 '§[a1g(og)]];[(4S1-3d12)+(452~3d22 )]J%(01+02+03+O4+05+06+O7+08) 0.354 1 1 ' §[blg(0)] fi<3d§<2_y2+3d)2(2_y2) J'8—(01-02+03+U4+65-06+O7-08) 0.220 . 1 1 2 :[b2g(;r)] 35(3dx y+3dx y) . . . . . . . 1 1 2 .1(01'03+05'07) 0-127 §I[eg(0)] If<4px - 4px) i . 1 _ 2 _. _ _ EII[eg(O)] Tf(4py 4Py) 2(02 04-1-06 08) 0.127 :I[eg(7r)] 3-2—(3d;z+3d)2(z) . . . . . . . 1 1 2 §Il[eg(7r)] ~72<3dyz+3dyz) . . . . . . 1 32.01)] nap; + 492 0. 0-034 1 1 §[a2u(02)] 72-(4p; 1' 4pZ) TZ—(Og'olo) 0.090 §[a2u(03)] %[(4Sl+3d12)-(452+3d§2)] OZ 0.355 1 1 §[a2u(04)] §[(451+3d12)-(452+3d:2)] 33(09-610) 0.177 1 1 §[a2u(05)] El:(481-36.;2)‘(452-3d32)17'8-(01+02+O3+O4‘05-O6—07—08) 0.354 1 1 _ 2 §[b1u(7T)] 72(3dxy 3dxy) . . . . 1 1 §[b2u(0)] J§(3d12_ -y2 2-3d:2_y2) J§(01-02+O3-O4-05+06-O7+08) 0.220 A 1 1 1 2 1 0 127 I[eu(0)], 33(4PX + 4px) 2(01-03-05’r07) - 1 1 I[eu(0)]~J§(4P;'+ 4P?) §(OZ—O4_OG+OS) 0-127 §I[eu ( )1 find);- 3d2 Z) ‘er 0.086 1 1 _ 2 TII[eu (F)! J213dyz 3dyz) WY 0.086 51 Table IV.1 The group overlap integrals (Gi.'s) for the u— amido-decamminedicobalt(III) ion in terms of atomic overlap-integrals-(Si.'s)a’b. G[a19(01)] = Gla2u(02)] = S(20, 4pc) G[a1g(62)] = G[a2u(o4)] = (J2/2)[s(2o, 4s) + s(2o,3do)] G[a1g(og)] = G[32u(05)] = (J2/2)[2s(2o, 4s) + S(2O,3dO)] G[a2u(01)] = (28(2p0. 4pc) G[a2u(O§)] : S(2pO, 45) + S(2pO,3dO) G[b1g(O)] = G[b2u(o)] = J3s(2o,3do) G[eg (0)] : o[eu (0)] = _f2s(2o,3do) G[eu (3)] . = rJ28(2pv,3dW) aThe molecular orbitals referred to in the Gi.'s are defined in Table II. ' ——l- bThe atomic overlap of orbitals i_and j is written as Si' = S(i,j); orbtial 1 refers to ligand atomic orbitals and 1 refers to cobalt atomic orbitals. 52 Evaluation of the Atomic Overlap Integrals (S..'s) - The __£l___ atomic overlap integrals needed for determination of the 511:8 were evaluated by use of tables giving overlap inte— gral values (henceforth, overlap tables) and master formulae given in the literature76'119'120. The relevant radial func- tions from Table II were substituted in the expression: and the equation expanded. Each term was then evaluated by use of the overlap tables or master formulae. The overlap tables are given as functions of the two parameters p and t; (H- + Du) R — _1____l .._ p— 2 a0 (5A-7) H-‘Li t= 1+ 3 Hi LL]. where ui and ii are the STO exponents of orbitals i_andpi (Hi > E1), g_is the bond length in A, and in is the Bohr ,radius (0.529 R). The overlap tables and master formulae given by Jaffe and Doak12° for 55 and 5p orbitals Were used in the calculation of 4s and 4p overlap integrals, since their tables and formulae were calculated with the . . . . . *- assumption of an effective principle quantum number, n , of 4. The use of an effective quantum number was unneces- sary for the 4s and 4p orbitals, because the radial func— tions were calculated independently114'115. A detailed out- line of the calculation of a typical overlap integral has been given by Bedon, gt. 1.70. The values obtained for the . , . . Si' 5 are listed in Table V. Table V. 53 Atomic overlap integrals (Si.'5). Overlap Integrala Typeb Value S(20,4s) e 0.187 S(20,4pO) e 0.090 S(2O,3dO) e 0.127 S(2O,4S) a 0.071 S(20,4pO) a 0.043 S(20,3dO) a 0.179 S(2p0,4pO) b 0.034 S(2p0,4s) b 0.251 S(2pO,3dO) b 0.104 S(2pv,3dw) b 0.061 aThe Si.'s are written as S(i,j) where i_is the ligand atomic orbital and j_is the cobalt atomic orbital. b - equatorial, with R = 2.05 R; 20 has 5.9% 25 character. - axial, with R = 1.70 R, 20 has 9.5% 25 character. — bridging, with R = 2.20 R; 20 is a pure 2p orbital. IU W’lm 54 Valence State Ionization Energies (VSIE) - The VSIE for the cobalt 3d,45, and 4p orbitals were estimated by means of the procedure outlined by Ballhausen and Gray121. The data for the cobalt yggg given by Ballhausen and Gray121 were used to determine the values of A, B” and §_in the equation: VSIE = qu + Bq + c (SA-8) (where q_is the charge on the cobalt atom) for different starting configurations. The values of fin.§1 and g are listed in Table VI for the different starting configurations. The values of the coulomb integrals H(3d), H(4s), and H(4p) (9-s-p-q) were then calculated for an assumed configuration 3d 45S 4pp with the charge q.= 9-gfsfp_from the relationships121: - H(3d) = 3d VSIE = (1-s-p)(3d VSIE:3d9) + s(3d VSIE: 3d8 4s) + p(3d VSIE: 3d8 4p) (5A-9a) _ = = _ _ . 8 H(4s) 4s VSIE (2 5 p)(45 VSIE. 3d 45) (SA-9b) + (s-l)(4s VSIE: 3d7 452) + p(4s VSIE: 3d7 4s 4p) - H(4p) = 4p VSIE = (2-5—p)(4p VSIE: 3d8 4p) (5A-9c) + (p—1)(p VSIE: 3d7 4p2) + s(4p VSIE: 3d7 4s 4p) where the y§l§_on the right side of the equations are calcu- lated from the data in Table VI. Equations (9a)-(9c) repre- sent an averaging over the different configurations; the sum of coefficients on the right side of each equation is unity. Ligand y§l§_were calculated from the data given by Ball- hausen and Gray121 for neutral N atoms. The coulomb integrals of the equatorial and axial nitrogen gforbitals were calcu- lated from equation (2)., 55 Table VI. VSIE functions for cobalta. Starting VSIE Configuration A B C 3d 3d9 13.05 91.15 44.80 3d 3d345 13.85 106.25 75.60 3d 3d84p 13.85 105.55 88.40 45 3d34s 7.25 66.65 59.10 45 3d74s2 7.25 75.75 70.50 45 3d7454p 7.25 71.35 84.00 4p' 3d84p 7.55 51.95 30.70 4p 3d74p 7.55 60.65 40.70 4p 3d74s4p 7.55 60.65; 40.80 aVSIE(q) = qu +-Bq + C; values of AJ B and g_are in units of 1000 cm.-1 56 The VSIE data of Ballhausen and Gray121 were calculated from Moore's atomic spectral data79. The method of calcula- tion has been outlined in detail by Bedon, gt. al.7°. Energy Calculations - The one electron energy levels of the Mgfs were calculated by the solution of the secular deter~ minant: Hij - ECij = 0 (5A-10) Because the symmetry properties of the molecule were used in the construction of the group orbitals, the secular determinant was factored into a series of low-ordered deter- minants: 2 x 2 in the case of the a1g(O3), b1g(O), eg(0), a2u(01), b2u(O), eu(O), and eu(w) orbitals; 3 x 3 for the alg(01) and a1g(02) orbitals; and 4 x 4 for the remaining a2u(O) orbitals. The 25 orbital on the bridging nitrogen (which trans- forms as the a representation) was not considered in the 19 final energy calculation. In general, the amount of mixing of atomic orbitals in an M9 is roughly proportional to the overlap and inversely proportional to the coulomb energy - H..)66. The overlaps of the 2s orbital _11. on N with the cobalt a b 1g difference (Hii orbitals J%(4p; — 4p:) and -%[(4s1 + 3dé2) + (452 + 3d:2)] were found to be small (0.016 and 0.032, respectively), and the coulomb energy dif- ferences between the 25 orbital and the cobalt orbitals are very large (over 110,000 cm._1). Preliminary calculations including the 25 orbital verified the conclusion that the 57 25 orbital does not significantly enter into the bonding in the decammine ion; therefore, the 25 orbital was not consid- ered in the final energy calculation. The values of the cobalt orbital coulomb integrals for the final calculation were calculated assuming a charge, g, of +0.25 and a configuration of 3d3'254s°°154p°'35. Ball- hausen has shown122 that Yamatera's Mg_treatment of the hexamminecobalt(III) ion98 results in a net charge of +0.30 on the cobalt atom. It was therefore decided that a g value not much different from 0.30 should be used. In addition, the criterion given by Gray and Ballhausen66 i.e. that the order of the coulomb energy should be O(ligand) < nd(metal) < (n+1)s (metal) < (n+1)p(metal) was taken into considera- tion. Calculations of the coulomb energies for different values of g indicated that the values based on g = +0.25 were the most reasonable. The coulomb energies are listed in Table VII. The coulomb energy of the cobalt 453dzz hybrid was calculated from equation (2). The nitrogen coulomb energies were taken as the nega- tive of the y§l§_of the neutral atom, as discussed above. The values are also listed in Table VII. The resonance integrals, H11} were estimated from Ballhausen and Gray's geometric mean equation64: H.. = F 5.. JH.. H.. (SA-11) 1) 13 11 33 with a value of -2.0 for F_in accordance with Ballhausen and Gray64 and other author569'70'71'34. Cotton and Haa58° have 58 Table VII. Coulomb energies used in the Mg_calculationsa. Cobalt orbitalsb.— H(3d) = -90.16 H(453d22) = -81.94 H(4s) = -73.71 H(4p) = ~38.09 Nitrogen orbitals.- H(2s) = -206.36 H(2p) = —106.36 H(20) = -112.26 (equatorial) H(ZO) = -115.86 (axial) a . . . —1 Energies in units of 103 cm. . bCalculated from equations (5A-9a)-(5A-9c) assuming a charge, q, of +0.25 and a cobalt configuration of 3d8'254s°-154p°°35. 59 shown that an‘g value of -2.0 results in a low value of 10Dq, in the hexamminecobalt(III) ion and recommend an §_value of -2.30. However, they found that an F value of -2.00 gave the best agreement in the case of the hexamminecobalt(II) ion. The §_value used in the present calculation should not seriously affect the relative ordering of the energy levels. However, because of the §_value approximation and other approximations discussed above and in Section IIIA, agreef ment of calculated and experimental energy differences would be fortuitous. B. Vibrational Analysis Calculations (Normal Coordinate Analysegl The normal coordinate analysis calculations were per- formed on the Control Data 3600 computer installation of the Michigan State University Computer Laboratory. The FORTRAN program used to perform the calculations was obtained from Dr. L. B. Sims, and is derived from a program written by Schachtscheider123v124. The program requires the following input data: a) The atomic positions (spherical polar or Cartesian coordinates). b) The internal coordinates (bond stretching, valence angle bending, out—of-plane wagging, torsional, linear valence angle bending, and in-plane wagging). c) A potential field of the generalized valence force field type (gygg), consisting of interaction con— stants between internal coordinates. 60 The §_matrix is calculated from the equation: 5 = B 3‘1 13' (SB-1) where g:1 is the diagonal matrix of the reciprocal atomic masses, and g is the transformation from the Cartesian dis- placement coordinates ézto the internal coordinates E} B = BE (SB-2) The 2 matrix elements are computed by the Wilson Sevec~ tor technique87r125. The displacements of the atoms are described by use of atomic displacement vectors, one for each atom, so that the internal coordinates are given by: n _$ _$ 3n Rk-rza 8.. - p. - .2 8.x. (5.-.) t—1 i-1 where S:I is the vector describing the displacement of atom E_and the p: is the unit displacement vector of atom E, The three Bki's belonging to atom E are the components of the > vector Skt° Wilson's unit vector 52j125 along the bond between atom .1 and atom j_is expressed in terms of the Cartesian coord- inates of these atoms: E: - [(Xj-Xi) 1>+ (Y 7> —> 'j j—yi) j + (zj-zi) k 1/rij (SB—4) where r.. is the bond length and i>, i? and k) are unit 1 J _ —- vectors in the x” y_and g_directions. The §fvector5 are then computed by use of Wilson's formulae87'125. For bond stretch— —> ing between atoms i_and j, the S are: kt 61 §> _ —-> ki ' ‘eij (SB-5) —> —> Skj :_ eij . —> . ' For the bending of the angle Qi.l the Skt for atoms A” jJ and l are: cos SI -'E> E2 = Qijl ji jl ki - . rij Sln Qijl (SB-6) E’ -E’ §> = COS Qijl jl ji kj rjl Sin Qijl —>- _ —> —> ) Skl ‘ ‘(Ski + Skj . 0 I ' where Qi.l # 180 . The three Bki s belonging to atom t are then taken as the xJ y, and §_components of the Sit and the §_matrix is computed from equation (1). The solution of the secular equation (see Section IIIB): sEL=LA Mew is obtained by diagonalizing the product 2 §:by use of the Jacobi method for symmetric matrices126. Although g:§:is not symmetric, the solution may be accomplished by solving two symmetric problems123t124v127. Consider the solution of sB=2£ Gem where 2:15 the eigenvector matrix and gzis the diagonal eigenvalue matrix of g, Since §_is real and symmetric, 2 is the orthogonal and the roots are real and positive; then: s=BIB Gem 62 Let g:be a matrix defined as: E = 21/2 B (SB-10) Then: 5 = H E‘ (SB-11) If a matrix ER defined by: E = 11' El»: (SB-12) is considered, the secular equation (7) may be written as: 11.9 =54 (SB-13) where 2.15 the orthogonal eigenvector matrix of H_and‘¥g is the diagonal eigenvalue matrix of H, The elements of {Ezare the Ai, which are related to the vibrational frequencies, Vi by: Vi = (1/2 w c) J7; (53-14) 1 The eigenvector matrix in equation (7) is given Nb by123,124,127: (SB-15) lb ll IS I0 and its inverse by: L = C w (SB—16) The transformation matrix 2“ which gives the Cartesian displacements of each atom in each normal coordinate Qi’ is computed from the equation123'123: ._ —1 1=M1§'E£A. (513—17) where all the matrices have already been defined. The computer program, as obtained, was suitable for performing vibrational analyses on molecules of up to 12 atoms. In order to perform the calculations on the decammine 63 ion (13 atoms), the calculations of the L_and T_matrices were eliminated. The vibrational analysis of the decammine ion was per— formed by separating the system into the linear (D4h) skele- tal structure and three sub-molecules with the appropriate local symmetry. Thus, normal coordinate analysis calcula- tions were performed for the decammine ion skeletal vibra- tions (all hydrogen atoms disregarded); the cobalt-ammine (Co-NH3) vibrations for equatorial and axial positions; the amido-bridge (Co-NHz—Co) vibrations; and, for consistency, the hexamminecobalt(III) ion skeletal vibrations. In the above systems, the pattern of the observed Spectrum was fit with diagonal force constants only (except for the hexammine- cobalt(III) ion). The neglect of hydrogen vibrations in the treatment of the skeletal vibrations of the decammine and hexamminecobalt— (III) ions (and vice versa) is justified by the frequency separation of the vibrations129: the vibrations involving the ammine ligands occur at over 800 cm.-1, while the skele- tal vibrations occur below 550 cm.-1. For each system, symmetry coordinates were used in order to take the symmetry properties of the molecules (or sub— molecules) into account. The use of symmetry coordinates also removed the redundant coordinates present in each system. The matrices in equations (7) through (16) are then replaced by the apprOpriate "symmetrized" matrices as described in Section IIIB. 64 The Cobalt-Ammine (Co-NHR) Systems - The structure used for the cobalt—ammine system is shown in Figure 4. The angles were assumed to be tetrahedral and the bond length R(N-H) was taken as 1.02 3103. The cobalt-nitrogen bond length was taken as 2.05 R for the treatment of the equatorial cobalt-ammine system and 1.70 R for the axial cobalt-ammine system2°. The system (equatorial or axial) contains ten internal coordinates (see Figure 4): 4 bond stretching co- ordinates (r1, r2, r3, r4), three H-N~H angle bending co- ordinates (212! 213! 923) and three H—N-Co angle bending coordinates (911! 922/ 233)° The potential field was of the G222 type and only diagonal force constants were used: 2 2 2 2 2 2v = Fr(r§+r§+r§) + F;(r4) + Fa rH (012+013+023) (5B-18) O H CO where Fr and F'r are the stretching force constants for the N-H and N-Co bonds respectively, and rH and rCO are the equilibrium N-H and N—Co distances. The symmetry of the Co-NH3 system is C3v' The symmetry coordinates are shown in Table VIII and are similar to those given by Nakagawa and Mizushima1°6. The U_matrix (see Section IIIB) is obtained from the coefficients of the internal coordinates in the expressions for the symmetry coordinates. All the vibrational modes (the Si) shown in Table VIII are infrared and Raman active. Figure 4 . Figure 5. 65 r4 Co Structure and internal coordinates for the normal coordinate analysis of the cobalt-ammine system. R(N-H) - 1.02 A, R(Co-N) = 2.05 A (equatorial or axial), all angles tetrahedral (109°28'). Only representative angle bending coordinates are shown. r 'n.-”. r A Q \B / AB C 0 Structure and internal coordinates for the normal coordinate ana ysis of the amido-bridge system. R(N-H) = 1.02 , R(Co-N) = 2.20 R, Q(H-N-H) = 1000, a(Co-N-Co) = 144°. Only representative angle bending coordinates are shown. Table VIII. Symmetry coordinates for the systems (C3v symmetry). 66 cobalt-ammine Spec- Vibra- ies tional Symmetry Coordinate Description Mode A1 S1 (1/J3)(r1+r2+r3) symmetric N—H stretch 82 r4 symmetric Co-N stretch S3 (14f6)(012+013+023‘014‘024'034) symmetric deformation E 54a (1/2)(2r1— r2- r3) assymmetric N—H stretch S4b (1/-J2)(r2 - r3) 35a (1/2)(2012-Q13-023) degenerate deformation 55b (1%f2>(613-023) s6a <1/2)(2614-oz4-034) J— rocking s6b (1/ 2)<624-634) 67 The Amido-bridge System (Co-NHz-Co) - The structure used for the amido-bridge system is shown in Figure 5. The Co-N bond length and the Co-N-Co bond angle were taken as 2.20 R and 144°, respectively20; the N-H bond length was taken as 1.02 R (as above) and the H—N1H bond angle was approximated as 100°. The amido-bridge system also has ten internal coordinates (see Figure 5): 4 bond stretching coordinates (r1, r2, rA, r - one H-N-H angle bending coordinate (0 ); one Co-N-Co B), angle bending coordinate 12 (GAB); and four H-N-Co angle bend— ing coordinates (a a 1A' fi'fli’ifl The potential field was of the GVFF type and only dia- gonal force constants were considered: 2 2 2 2 2 2 2 2 = + + ' + + + ' 2V Fr (r1 r2) Fr (rA rB) Fa rH (012) F0 rCo(QAB) (SB-19) + " + + + Fa rH rCo (01A OZA 01B 0‘2B) where F and F' are the stretching force constants, F , F' ._£ ..E ._Q .41 and F" are the bending force constants, and r and r are _Q. - _H_ Co the equilibrium N-H and N-Co distances. The symmetry of the bridge system is C and the sym- 2v metry coordinates are shown in Table IX (similar coordinates have been given by Nakagawa and Mizushima1°6). All the vibrational modes are Raman active, but only the A1, B1, and B2 modes are infrared active. The Hexamminecobalt(III) Ion - The normal coordinate analysis calculationsfor the hexamminecobalt(III) ion were done with 68 Table IX. Symmetry coordinates for the amido-bridge system (C2V symmetry). 'Spec- Vibra- ies tional Symmetry Coordinate Description Mode A1 S1 (1/f2)(r1+r2) symmetric N-H stretch 82 (1/~f2)(rA + rB) symmetric Co—N stretch S3 (1/V20)(4&12—01A-02A-01B-02B) NH2 bending S4 QAB Co-N-Co bending ._ _ + ° ' A2 85 (1/2)(a1A 02A 01B 02B) NHZ tw15ting B1 56 (1/f2)(rA - rB) assymmetric Co~N stretch S7 (1/2)(01A+OZA-G1B-02B) NHZ wagging B2 S8 (U02)(r1 - r2) assymmetric N-H stretch $9 (1/2)(01A-02A+01B- 02B) NHZ rocking 69 the internal coordinates and symmetry coordinates given by Shimanouchi and Nakagawa1°9. A Co-N bond length of 2.05 A was assumed103. The potential field was of the gygg type; in addition to the diagonal force constants, the off-diagonal interactions between Co-N bond stretching coordinates were used in the calculations: 6 6 6 2V = F 2 r2 + F , Z r. r. + F r2 2 Q2. (5B-20) 1 i=1 1 rr i>j=1 1 3 ° i>j-1 where FI and EQ are the diagonal stretching and bending force constants respectively, Frr' is the off-diagonal stretching interaction constant, and rN is equilibrium Co—N distance. The hexamminecobalt(III) ion calculations were used as a check on the force constants used for the decammine ion. The vibrations of the octahedral hexamminecobalt(III) ion transform in Oh as: TV = Alg + Eg + 2Tlu + ng + T2u (SB-21) The Alg' Eg’ and T29 Vibrations are Raman-active and the T2u vibration is inactive; only the two T vibrations (an as- lu symmetric bond stretching and an angle deformation symmetry coordinate1°9)are active in the infrared. The uramido-decamminedicobalt(III) Ion - The linear (D4h) structure used for the decammine ion in the Mg calculations was also used in the normal coordinate analysis calculations. The bond lengths were approximated from Vannerberg's datazo: = 2.20 R. R(Co-Ne) = 2.05 R; R(Co-Na) = 1.70 R; R(Co-Nb) 70 Thirty-six internal coordinates were used in the calculations- twelve bond stretching coordinates and 24 angle bending co- ordinates. The bond stretching coordinates were of three types: equatorial, axial, and bridging Co-N bonds. The angle bending coordinates were also of three types: Ne-Co-Ne, Ne-Co-Na, and Ne-Co—Nb bond angles. The structure, bond stretching coordinates, and representative angle bending coordinates are shown in Figure 6. The potential field was of the gy§§_type, and only diagonal force constants were used: b 2 2 2 2 2 2 2 2 2 2 2 2 r(r11+r12) e a 2 = F r +r +r +r +r +r +r +r + F r +r + F V r( 1 2 3 4 5 6 7 8) r( 9 10) 2 2 2 2 2 2 2 2 + F I:(012+023+O34+014+056+Q67+O78+058) 2 ,2 2 2 .2 _2 ,2 2 + F re ra(019+029+039+O49+05,10+Q6.10+°7.10+08.10) 2 2 2 2 2 2 2 2 r rb(91,12+02,12+Q3,12+Q4,12+05’12+Q6’12+Q7’12+Q8’12) e (5B-22) + F Q U Q m Q m where F:, F:, and F: are the stretching force constants; Fe, F2, and F: are the bending force constants; re, ra, and .2 r are the equilibrium Co-Ne, Co-Na and Co-N distances, b U! respectively. Three internal coordinates were not included in the calculations: the two linear bending coordinates connected with the Co-Nb-Co bridge and the torsional coordinate between the two connected Co-N5 groups. The symmetry coordinates for the decammine ion (in D4h) are shown in Table X. The vibrational modes are listed in 71 mamcm m>flumucmmmumwu maco .oowa I AMZIOUIQZVO n AOUI n Anzuooamzvo IAQ GCOQ $39 .QBOQm mum mmumcflouoou mcflpcmn Q n AmZIOUIwZvo u AmZIOUImZVo "mum mmamcm mQB zlouvm “m o>.H n Amzuoucm “m mo.m I Amzlouvm "mum ZIOUVU “com .m ON.N mnpmcma .COH AHHHVpaMQOUHUmCHEEmomUIOUHEmLm mnu mo mflmmamcm wwmcflpnoou HmEHoc mzu How mmumgflpuooo Hmcnmucfl pom musuosuum .m mndmflm 0 my 00 «HM Z [‘ mud 0 Z HHH II 00 mH / HH.HU L my mad 72 Table X. Symmetry coordinates for the gfamido-decamminedi- cobalt(III) ion (D4h symmetry). Spec- Vibra- ies tional Symmetry Coordinate Mode 1 A21.1 81 R(r1+r2+r3+r4_r5-r6-r7"r8) 1 52 ,Jfiirs ’ r10) S 1 3 AT§KI11 ' r12) 1 S4 ‘Z<019+029+039+049*01,12‘01,12‘02,12‘04,12 "05.10-06.10”O7,10’08,1o+05,12+06,12+07,12+ag,12) (rl-ra-r5+r7) (rz-r4—r6+r8) (012'034‘056+078) (023-014-067+058) U) 03 U th th th th th NHA th 87a (019-039-05,10+Q7,10) 37b (029-049‘06,1o+08,1o) 88a (O1,12-03,12-05,12+Q7,12) A S '—l(r +r +r +r +r +r +r +r ) 1g 9 VF8 1 2 3 4 5 6 7 3 s 1(r + r ) 10 {7'2 9 1° 1 311 q§(r11 + r12) 1 + + + - ~ 12 2(019 029 039 049-01,12‘02,12‘03,12‘04,12 +05,1o+06,1o+07,1o+08,10‘05,12"06,12"07,12‘08,12) 73 Table X. (Continued). Spec— Vibra- ies tional Symmetry Coordinate Mode . B S 1 1g 13 J§(r1-r2+r3-r4+r5—r6+r7-r8) S l 14 4(019‘029+039‘O49‘01.12f02.12‘03,12+04,12 +05,10‘06,10+0’7‘,10"08,10‘05,12+06;12"O7,12+03,12) B S 1 2g 15 'J§(012-023+Q34-014+056-Q67+Q78-058) E S -l(r -r +r -r ) g 16a 2 1 3 5 7 l S16b 2(r2-r4+r6-r8) l S17a 2(a12_034+056'078) l Sl7b 2(023'014+067'058) l_ . S18a 2(019_039+05,10‘07,1o) l Slgb 2(029‘049+06,10'03,1o) s l 19a 2(01:12‘03.12+05,12‘07,12) s l 19b 2(a2112-Q4:12+06,12-Q8,12) B S 1 In 20 ,J§(Q12-QZ3+034-Ql4‘056+067'078+Q58) B S 1 2u 21 J§1r1‘r2+r3‘r4‘r5+r6'r7+r8) s .1. 22 4(019'029+039-049‘O1,12+02,12‘03,12+O4,12 “05,1o+06,10'07,1o+08,1o+05,12—06,12+O7,12‘Q8,12) 74 order of their activity: infrared - A2u and Eu; Raman - A1 I g B , B , and E ; inactive - B and B 19 29 g 1u 2u° VI. RESULTS AND DISCUSSION A. Synthesis The compound E—amido-decamminedicobalt(III) nitrate (decammine nitrate) was prepared following Werner's pro— cedureszr19. A problem arose in connection with the reac- tion of the ufamido-Efsulfato-octamminedicobalt(III) nitrate ("sulfato nitrate") with concentrated hydrochloric acid (reaction 3, Section IV). Repeated attempts to remove the sulfate bridge under a variety of conditions (heating, dif— ferent acids and acidities) failed when the pure sulfato nitrate was used. However, when the crude sulfato nitrate (see Section IV) was used in preparation, the reaction proceeded without complications. The difficulty in react— ing the pure sulfato nitrate is apparently due to it being in microcrystalline form, which does not dissolve easily in acid. The compound [H20(NH3)4C0NH2CoCl(NH3)4]Cl4 ("Chloroaquo chloride") obtained from the crude sulfato nitrate was therefore also used in the crude form. The contaminant is most likely the hexamminecobalt(III) ion (see Section IV). Attempts to purify the Chloroaquo chloride generally resulted in precipitation of the contaminant with the product. In some cases (recrystallization from water), the contaminant remained in solution, but a mixture of a purple-red compound (Chloroaquo chloride) and a blue-red compound (thought to be 75 76 E7amido-Erhydroxo-octamminedicobalt(III) chloride) was obtained. In only one case was the purification successful; the pro— cedure and analytical data are reported in Section IV. The reaction of the crude Chloroaquo chloride with concentrated nitric acid produced the compound [(N03)(NH3)4CONH2COC1(NH3)4](N03)3 ("chloronitrato nitrate") in crude form (reaction 4, Section IV). Attempts at purifica— tion by various means failed; therefore the crude form was used in the preparation of the decammine nitrate (reactions 5 and 6, Section IV). The successful preparation of the decammine nitrate tends to verify the formulation of the chloronitrato nitrate. B. Electronic Spectra The electronic spectral data for the bridged compounds prepared in this investigation are given in Table XI. The perchlorate salt of the uramido-Efsulfato-octamminedicobalt(III: ion was prepared by treatment of the sulfato nitrate with 70% perchloric acid. The spectrum of the chloronitrato nitrate was determined by use of a crude sample, so that the reported molar absorptivities are less than the actual values. The bands in the spectra of the decammine nitrate and the Chloroaquo chloride were analyzed by fitting them to a gaussian error-curve130 of the form: v - v e — emax exp [-(fi‘fifi (SB—1) where e and e are the molar absorptivities at v and v - max —- max and 9 is given by: 77 Table XI. Electronic Spectra of some bridged complexes. Sol- Vmax‘ Molar Compound vent x10 3 Absorp- cm. tivity [(NH§)5CONH2CO(NH3)5](N03)5 H20 19.74 412 28.01 729 38.90 22000 0.1N 19.74 409 HNo3 27.93 673 38.83 22000 [H20(NH3)4CONH2COC1(NH3)4]Cl4 0.1N 14.20 57 HCl a 20.32 169 33.9 3340 [No3(NH3)4CQNHZCOC1(NH3)4](No3)? H20 14.39 (39) 20.66C (152) 33.8 (2580) [(NH3)4CO(NH2,SO4)CO(NH3)4](C104): H20 18.69 230 27.25 401 (36)e (3000)e 3+ f [Co(NH3)6] 21.05 60 29.50 55 aBroad band, see Figure 8. Spectrum determined using crude compound; absorptivities are therefore low. Shoulder. Data from reference 91. H1004!) Similar to band in Chloroaquo chloride (Figure 8). Prepared by treatment of the nitrate with 70% HClO4. reported molar 78 9 = 8/1n 2 (6B-1a) where g_is the half-width of the band. The oscillator strength, _§, of each band was obtained from the relation130: 9 f = 9.20 x 10 - Emax 8 (63-2) In the case of the first band of the decammine nitrate (vmax _ 1 . = 19,740 cm ) and all the Chloroaquo chloride bands, an unsymmetrical gaussian error-curve was assumed in order to fit the band: different half-widths, 6(+), and 6(-) for v > v and v < v '— max —- max’ reSPeCtiV91Y. were used. The oscil- lator strength was calculated from equation (2) Where 8 is replaced by %(§(il +_QL;)). The spectrum of the decammine nitrate is shown in Figure 7 (solid line). The dashed curves indicate the curves calcu— lated from equation (1). The parameters used for the Gaussian analysis are shown in Table XII. In the case of the decammine nitrate, the band in the ultraviolet region (Vmax : 38,900 cm._1) could be resolved into two bands (IIIa and IIIb in Table XII). It is probable that a weaker third band at a lower frequency contributes to the observed band, since the low frequency end of the band could not be fitted exactly with Bands IIIa and IIIb. The spectrum of the Chloroaquo chloride is shown in Figure 8 (solid line) along with the resolved curves (dashed curves). -No attempt was made to analyze the band in the ultraviolet (vmax = 33,900 cm.-1) since it is actually a shoulder on a much more intense band. The parameters obtained from the gaussian analyses are shown in Table XIII. 79 .wammamcm amammsmm mo UHSmmH may mwumoapcfl mafia Uwflwmp “Esuuowmm HmucwEHmexm mzp ma mafia Uwaom . 50 .kum3 Ca mumuuac AHHHVpamQOUHUwcHEEmUmUIOUHEmLfl mo Esnuuwmm oaconuuwaw 6:9 b on Hm HI.EU mOH .mucmdwwnm 3 mm mm 1 I\ 1 6w // q _ \ / / \ / / \ 3- / I . / \ z , 0 \ z 1 9N1. / x . . y Y , 3%. t x V .l r .1 V t .1 p t - .8 m8. 3 1.. 4 b A a 0 II Moom OOQI 1 cm 80 Wavelength,mu 400 500 600 70f Sol 4——-150 '4 I l \ \ /\ ’ I / I ’ I I I I I I I I ‘ , \. I I \ , I I I II I‘ 100 I \I I ‘ I I I ‘I I I II I I y I I I I I\ I I I ‘ ‘ I I ’ I I I I ' I I I I I \ I I ) ) / \\ 50 I I \ " I \ I I / I ‘ I ’ ‘1 I I \ I I I “ I \ I I ‘ \ / \ I I ‘ \\ / \x , / \ \, \ I \ V \\ I ” \ /\ \ / I \\ l/ \s 1 \\s . ./ ~{” , \\’/ \ 25‘ 20 _1 15 12 Frequency, 103 cm. Figure 8. The electronic spectrum of the Chloroaquo chloride ([H20(NH3)4CONH2COC1(NH3)4]C14) in 0.1N HCl. The solid curve is the experimental spectrum; the dashed curves are the resolved bands. Molar Absorptivity 81 Table XII. Parameters for the gaussian analysis of the . electronic spectrum of [(NH3)5C0NH2C0(NH3)5](N03)5 in water. Band Vmax €max (oiaéft)?§?'))l fa x10-3 cm._1 cm.-1 I 19.8 420 1700,1450 0.006 II 28.0 690 1900 0.012 IIIa 38.8 14000 2800 0.36 IIIb 39.3 7500 1600 0.11 aOscillator strength, from equation (6B-2). Table XIII. Parameters for the gaussian analysis of the elec- tronic spectrum of [H20(NH3)4C0NH2C0C1(NH3)4]Cl4 in 0.1N HCl. V max Band x10‘3 cm.'1 Emax 6(+)Cm.-f(—) fa 1 14.2 56.9 1300 1000 6 x 10‘4 II 18.5 135. 1450 1400 1.8 x 10"3 111 21.0 145. 1350 1300 1.8 x 10"3 aOscillator strength, from equation (6B—2). 82 C. Molecular Orbital Calculations: Results and Discussion Results - The results of the molecular orbital calculations are shown in Table XIV. The energies were caluclated by solving the secular determinant: H - EG. ij lj[ = 0 (6C-1) The values used for the Coulomb integrals (H. ) have been ii given in Table VII, and the group overlap integrals have been given in Table III. The resonance integrals (Hi.) were estimated from the relationship: H.. = -2.0 G..IJH.. H.. (6C-2) 1] 13 ll 33 The coefficients of the Mgfs were calculated by sub— stitution of the energy values in the secular equations: N 2 (Hij - EG. ) c. = 0 (j = 1,2,...,N) (6C-3) i-1 and application of the normalization condition: 2 : .. 2 Ci + 22 ci cj Gij 1 (6C 4) The population analysis was performed by use of the equation: ' = 2 I — POP (n1) cni +i§j cni cnj Gij (6C 5) (see Section IIIa). The input coulomb energies were calcu- lated for a cobalt atom charge of +0.25 and configuration of 3d8‘25 4s0'15 4p0'35; the population analysis of the results reported in Table XIV give a cobalt atom charge of +1.24 and a configuration of 3d6°94 450-46 4p°~36. The disagreement of input and output values of the charge and 83 Table XIV. Energy levels and molecular orbital coefficients for the Efamido—decamminedicobalt(III) ion. Calcu— .lated for a charge of +0.25 for the cobalt atoms (see Table VII). , . -E,' Molecular Orbital Coefficientsa Molecular x10—3 Orbitals -1 C3d C4p Ce Ca Cb cm. Ialg(o),Ia2u(0) 125.1 0.421 ... 0.770 ... ... IIa2u(0) 123.6 0.302 0.353 ... 0.748 0.297 Iblg(0),Ib2u(0) 121.8 0.444 ... 0.804 ... ... IIalg(o) 120.3 0.101 0.346 ... —1.006 ... IIIa2u(0) 115.2 -0.094 0.522 ... 0.664 -0.492 Ie (0),Ieu(o) 112.4 ... 0.031 0.996 ... ... Ieu(w) 109.0 0.358 ... ... ... 0.903 bzg(v),b1u(w),eg(w) 90.2 1.000 ... 1.. ... ... IIeu(w) 86.0 0.946 ... ... ... —0.417 IIIa1g(0) 71.4 0.964 0.089 ... ... 0.463 IIb1g(0),IIb2u(0) 70.4 0.425 ... 0.635 ... ... IValg(o),IVa2u(o) 41.9b 0.859 ... 0.900 ... ... Va1g(o) 36.9 ... ... ... ... ... IIe (0),IIeu(0) 36.2 ... 1.008 0.159 ... ... b Va2 (0),VIa2u(0) 33.7 ... ... ... ... ... a = . . . . c3d cobalt 3d orbital coeff1c1ent (sd hybrid for a1g and a2u orbitals); c4 = cobalt 4p orbital coefficient; ce : equa- torial gyorbital coefficient; ca = axial gforbital coeffici- ent; cb = bridge orbital coeffIEient (oz for a2u (0) orbitals, W and w for e (w) orbitals). '_— x ._y u bCoefficients not calculated. 84 configuration will be discussed below. The ground state con- figuration used for the population analysis is derived by assigning the 38 electrons of the system (12 from the 2 co- balt atoms, 6 from the bridging amido group, 20 from the 10 ammine groups) to the lowest lying orbitals: [[Ia (0),Ia2u(o)]4[IIa2u(0)]2[Ib1 (0),Ib2u(o)]4[IIa (0)]2- 1g 9 [IIIa2u(0)]2[e (0),Ieu(0)]8[Ieu(v)]4[ng(w),b1u(w),e 9 4 [IIeu(w)] 1 s [CORE]26[b2g(w),b1u(v),eg(v)] The molecular orbital energy level diagram that is proposed on the basis of the results given in Table XIV is shown in Figure 9. The proposed ordering in Figure 9 differs from the ordering obtained from the calculations only in the relative p031tions of the [IIb1g(0),IIb2u(o)] and IIIa1g(0) levels; the reasons will be discussed below. Bonding — The bonding orbitals are of some interest. The equatorial ammine groups (designated Ne) are bonded to the cobalt atoms through the Ia1g(0), Ia2;(0), Ib1g(0), Ib2u(0), Ieg(o), and Ieu(0) orbitals; these orbitals are similar in form to those obtained for gfbonding in octahedral compoundsl31, and require no further comment. The axial ammine groups (designated Na) are gfbonded to the cobalt atoms through a combination 6; the cobalt 4s3d: hybrids and 4pz orbitals in the IIalg(0) orbital. The 52 are also involved in the IIa2u(0) and IIIa2u(0) orbitals, Which also involve the cobalt-nitro- gen-cobalt bridge gfbonds. The IIa2u(0) has roughly cylin- drical shape which encompasses the Na-Co-Nb-Co-Na (Nb is the amido group) axis; from the relative magnitudes of the 85 4p 45 4s3dzz 3d Va2u(0).VIa2u(0) Va (0),IIe (0),IIeu(0) 19 9 IVa (0),IVa2u(0) 19 (O) IIIa IIblg(0),IIb2u(o) ) 20(equatorial)_ 2p(OziITXIITy 20(axial) Ialg(0),Ia2u(0) Co orbitals molecular orbitals ligand orbitals Figure 9. Proposed molecular orbital energy level diagram for the fifamido-decamminedicobalt(III) ion (not to scale 86 coefficients (Table XIV) it can be estimated that the two electrons in this orbital are located principally in the Co-Na bonds. The IIIa2u(0) orbital is also of cylindrical shape, but has a somewhat higher electron density in the Co—Nb bonds. It seems, therefore, that the Co—Naig-bonds acquire additional stabilization at the expense of the Co-Nb bonds; this accounts for the closeness of the axial ammine groups (1.70 X) in comparison with the equatorial ammine groups (2.05 8). The extra stability of the Co-Na g bonds also accounts for the relatively large Co-N distance (2.2 R); b apparently Efbonding adds very little stability to the bridge. The b2g(w), b1u(v), and eg(v) orbitals are non-bonding orbitals with the electron density completely localized in the cobalt 3d orbitals. The IIeu(v) orbital is an anti- bonding Eforbital with the electrons localized principally in the cobalt 3dxz’ 3dyz orbitals. The relative magnitudes of the coefficients given in ,Table XIV indicate that in almost all cases the bonds show appreciable covalency. Fenske84, however, has stated that "appreciable covalency is an automatic consequence of.the assumptions of the Mg method. Whether this conforms to physical reality is highly debatable." In the case of the decammine ion, it is indeed probable that the coefficients obtained in the calculation overestimate the covalency and that the bonding is principally ionic. Consideration of the relative magnitudes of the coefficients in the IIa2u(0) and IIIa2u(o) orbitals leads to the conclusion that the bonds 87 involved in bridging (the Co-Nb bonds) are more ionic than the cobalt-ammine (Co-Na or Co-Ne) bonds. It is probable that the assumption of sp hybridization for the gfbonding orbital of Nb ( calculations) would result in greater covalency in the rather than the pure pz orbital used in the Co—Nb bond (due to greater overlap); it is questionable, however, whether greater covalency would conform to physical reality. The proposed high ionic character for the Co—Nb bond is consistent with the chemical stability of the Co-NHZ-Co bridge system in spite of the relatively large Co-N bond length (2.2 R). b The Electronic Spectrum of the uramido—decamminedicobalt(III) lgg - The spectrum of the decammine ion is shown in Figure 7 and the numerical data are given in Tables XI and XII. The spectrum consists of two bands of moderate intensity with maxima at 19,740 and 28,010 cm.“1 (Bands I and II, respective- ly) and an extremely intense charge transfer band (Band III) at 38,900 cm._1. Bands I and II correspond to the two bands in the spectrum of the mononuclear hexamminecobalt(III) ion (see Table XI) and can be assigned as d —> d transitions. The intensities of Bands I and II are significantly greater than the intensities of the corresponding hexamminecobalt(III) band. It is therefore probable that the decammine ion bands are due to symmetry—allowed transitions (the hexammine- cobalt (III) bands are symmetry forbidden and acquire intensity from vibronic interactions). 88 The ground state of the decammine ion has been given in equation (6); the highest occupied orbitals (bzg(v), b1u(w), eg(v) and eu(7)) are all principally 3d levels and the transitions accounting for Bands I and II should originate from them. Consideration of the symmetry properties of the orbitals listed in Table XIV and the energy differences de- rived from the data in this table shows that only two transi— tions of the right order of magnitude in energy are symmetry (GMIA allowed: IIeu(w) —> IIb ‘5 1E3) and IIeu(V) ’9 19 19 IIIa (0)(1A —> 1Eb) (Ea and Eb are different excited 1g 1g u u u states having Eu symmetry). The relative ordering of the [IIb1g(0), IIb2u(0)] and the IIIa1g(0) orb1tals 15 therefore of great importance for the assignment of the transitions for Bands I and II. The M9 calculations reported in Table XIV are of little aid in this respect since the calculated energies of these orbitals are approximately equal; therefore other factors must be considered. The IIIalg(0) orbital is principally composed of the axially symmetric cobalt 4S3dzz hybrids, while the IIblg(0) and IIb2u(0) orbitals are principally composed of the cobalt 3dx2-y2 orbitals. From a qualitative crystal field viewpoint, it would be expected that the closer approach of the axial ammine groups (1.7 8) would destabilize the axially sym- metric 4S3dzz hybrids relative to the 3dx2-y2 orbitals. Thus ' l the ordering of the Mg_s would be a1g(0) > b1g(0), b2u(0). Bands I and II of the decammine ion spectrum are then assigned as follows: 89 a Band I: IIeu(w)-——> IIb1g(o) (lAlg-—> 1Eu) (6C-7) .__> 1E b 1g ) Band II: IIeu(W)-——> IIIa (6) (1A 19 The ordering arrived at above has been taken into account in the construction of the proposed Mg energy level diagram (Figure 9). The ordering of the 3d orbital levels in Figure 9 cor- responds to the ordering given in Figure(2c)for the case of axial compression for tetragonal Co(III) complexes. Each cobalt atom in the decammine ion is in a tetragonal environ- ment of C4v symmetry. The proposed ordering of 3d levels indicate that axial compression (by the axial ammine groups) is the principal tetragonal distortion in spite of the elongation exhibited by the Co-Nb bond. Bands I and II may be assigned as the sum of separate transitions on each cobalt atom. Band I would then be assigned as the sum of the two e —9 b (d d —> dx2_y2) transitions and Band II as the 1 xz’ Y2 sum of the e —> a1 (dxz’dyz —> d22)° This viewpoint (separ- ate d -> d transitions for each cobalt atom) may be profit— ably applied to the spectrum of the Chloroaquo ion (Figure 9, Table XIII), which will be discussed separately. The notation of the C4V symmetry group will be used henceforth in discussions involving the "separated transitions" view- point. The charge transfer band in the decammine ion spectrum (38,900 cm._1) is more easily assigned. Consideration of the orbital symmetries in the Mg_diagram (Figure 9) and the () (I) ( rn '1' 90 energy difference.derived from Table XIV lead to three allowed charge transfer transitions of the L —¢ M (reduction) type. In order of decreasing energy, the transitions are: .._ 1 1 IIIa2u(0) > IIIalg(0) ( Alg -> A2u) C Ieu(o) -——> IIIa1g(o) (1A1g —> 1Eu) (6C~8) d _ 1 _ 1 Ieu(v) > IIIalg(O) ( Alg > Eu) The observed charge transfer band can be resolved into two separate bands (Table XII); the disagreement in the ob- served and calculated line shape on the low frequency side of the band indicates that a third band at lower frequency is at least possible. The three bands would then be assigned to the transitions given in equation (8). It should be noted, however, that the two (or three) observed bands assigned as the charge transfer transfer transitions may not all be due to the decammine ion; since an extremely low concentration (about 3 x 10-5M) was necessary to observe the spectrum in this region, one of the bands may be due to an hydrolysis or decomposition product of the decammine ion. Thus, while the observed charge transfer band may be assigned as the sum of the transitions given in equation (8), it is not possible to specifically assign each resolved band. The effect of lowering the symmetry to C2V (Vannerberg's structurezo, Figure 1) on the above assignments must be ex- amined. The correlation of the D4h representations with C2V representations are obtained from the tables given by Wilson, Decius and Cross132; the principal axis is taken as the x 91 axis in Figure 3 (the Cé operation in D since this axis 4h) would become the major axis of the "bent" structure (Figure 1). One effect of the lower symmetry is the splitting of the E(D4h) representations: eg(D4h) —> a2(C2v) + b2(C2V), eu(D4h) —> a1(C2V) + b1(C2V). The other levels of interest (d levels) t f ' . _. _. rans orm aas follows in C2v' ng(D4h) > b1(C2V),b1u(D4h) > a b b —> b -> 2(C2v)’ 1g a1(C2v)' 21193411) 2 d transitions is, however, open to another, perhaps more realistic, inter- pretation: that the two halves of the molecule are relatively independent of one another and the transitions observed as Bands I and II are the sum of the e -> b1, and e -> a1 transim tions, respectively, on each cobalt atom (as explained above). The principle effect of the amido bridge would then seem to be the shortening of the Co-Na bond, producing an axially- compressed tetragonal perturbation on the d—orbitals. It is 92 not possible to generalize this effect (compression of the Co-Na bond),.since structural.data on other amido—bridged complexes are not available. The Value of q_and the SCCC Treatment - The output value of —_f the cobalt atom charge, q, in the decammine ion calculation was +1.24. This value would indicate that, if it were de— sirable to recycle the calculation to obtain self-consis- tency (the S999 treatment), a higher value of 3 should be used. Figure 10 shows the variation of the cobalt orbital coulomb energies (Hii) with q, and the relationship of the Hii's to the ligand coulomb energies for the series of cobalt o - 01 o 8 50 q4s0 54p0 35. As can be seen, at configurations 3d higher values of g, the 3d orbital coulomb energy (g(§§l) approaches and crosses the ligand coulomb energies (§1_p), etc.). The values of H(3d) at higher values of g would not conform to the criterion of Gray and Ballhausen66, that the coulomb energies should have the ordering 2g (ligand) < nd (metal) < (n + 1)s(metal) < (n + 1)p(metal). Thus the calcu» lations were not recycled to self-consistency, and the calcu~ lated energy levels are given only qualitative significance. The meaning of the value of 3 obtained in this and other investigations is far from clear. In no case has a charge value greater than +1 been found for any central metal ion, and in most cases the charge is found to be +0.6 or less (in a recent Mg_calculation for the hexamminecobalt(III) ion, Wirth133 has obtained a charge of +0.07 for the cobalt atom: ___,O H(4p) .._. 50 '. H(4s) E 0 . H(3d) .0 I o H x \ '"F -——~11OO H(Zp) a H(20) equatorial \\\\ Y \x H(20) axial 97‘ | l I l | 0 +0.1 +0.2 +0.3 +0.4 +0.5 Figure 10. Dependence of coulomb energies of the various orbitals on the charge (3) of the cobalt atoms. The circles represent the coulomb energies at 3.: +0.25 Which were used for the Mg_calculations. 94 he assumed the NHé ligands to be uncharged). In discussing the q value (+0.30) of the cobalt atom in the hexammine- cobalt(III) ion obtained from Yamatera's Mg_treatment93, Ballhausen has stated122 that "whereas in the ionic model the cobalt ion carries a charge of three positive units of electricity, these are now smeared over the whole complex, andtfluametal atom is nearly neutral. This result is in ac— cord with the charge-neutrality principle..." The low values of q obtained in Wolfsberg—Helmholz Mg_calculations would seem to indicate a high degree of covalency° But Fenske84 has observed that "appreciable covalency is an automatic consequence of the ... method." Thus, for the present at least, the charge q_must be regarded as a paramem ter having little physical significance. Coulomb energies derived in Sgg§_treatments by variation of g_should probably be rejected unless they conform to the Gray-Ballhausen criterion66. The overlap integrals used in M9 calculations might also be regarded as having little quantitative significance. The values obtained for overlap integrals are dependent on the wave functions used in the calculations: Wirth133 has shown the variation in the values of hexamminecobalt(III) overlap integrals that result from the use of different wave func- tions. The inclusion of ligand-ligand overlap also has a significant effect on group overlap integral value5133. Over- lap integrals must be regarded, then, as having at best qualitative significance and are a major obstacle to regarding 95 the Mg_theory as quantitatively significant. Wirth has shown133 that by the use of more accurate wave functions.and other input parameters and the inclusion of ligand-ligand overlap, the Dq value of the hexamminecobalt(III) ion may be calculated to within 10% accuracy. In treating complicated ions of lower symmetry, however, Wirth states that other effects, such as electron repulsion and configura- tion interaction, need to be taken into account and that "it is doubtful that the central approximations of the extended Wolfsberg-Helmholz approach are accurate enough to support these elaborate superstructures." Thus, the results of Mg_calculations using the Wolfs- berg-Helmholz approach should be regarded as being only qualitatively significant. An almost bewildering variety of approximations have been used in the various transitionw metal complex M9_treatments, yet the results are, for the most part, qualitatively consistent with each other and with the results of the crystal field theory. Assignments of d —> d transitions from the results of Mg calculations should be regarded as realistic only if they agree with crystal field treatments. It is only in the assignment of charge-transfer transitions that the Mg_theory clearly over— rides crystal field theory, since OFT can not account for them. The Spectrum of the Chloroaquo Ion — The two resolved bands in the Chloroaquo ion spectrum (Table XIII, Figure 8) at 18,500 and 21,000 cm.“1 may be assigned as the e —> b1 96 transitions (see Figure 20) for the two now—different cobalt atoms. The e-—> a1 transitions are masked by the charge— transfer band at 33,900 cm.-1. The equality of the intensi— ties of these two bands (see Table XIII) lend.a credence to assignment of the bands to the same transition on different cobalt atoms. These assignments also support the View ex- pressed above: that the two halves of the molecule are relatively independent and can each be treated separately as tetragonal systems with axial compression. (6 assigned as a singlet-triplet transition, in conformance 1 The band at 14,160 cm._ 57, see Table XIII) is with assignments in the mono-nuclear cobalt ammines92:101 (see Section IIIC). Thus the band is assigned as either the e —> b1 or e -> 31 transition in which the excited state is a triplet (3E). The high intensity observed for this band is rather sur— prising: in Co(NH3)5C12+ the corresponding band has a molar absorptivity of less than 192. However, the mononuclear iodo-and-bromopentammines also have high intensity singlet“ triplet bands (log e's of 1.48 and 0.67, respectivelygz). Jérgensen has attributed the high intensities to a delocalin zation effect in which a part of the large spin-orbit coup» ling constants of the heavy halogens is added to the small cobalt(III) spin-orbit coupling constant134. A similar ef— fect may be Operative in the Chloroaquo ion. Hydrogen bond— ing between the bound aquo and chloro groups would provide a mechanism for delocalization and would result in a greater 97 effective spin-orbit coupling constant (a similar mechanism may be Operative in the chloronitrato ion if an interaction between the chloro group and a nitrato oxygen is assumed). It is difficult to choose between the e —> hi, and e -> a1 assignment for the Singlet—triplet transition in the chloro- aquo ion. Linhard and Wiegel92 have shown that the frequen« cies of the two singlet-triplet bands (1A1 -> 3T1 and 1A1 -> 3T2) in the halopentammines decrease with increasing halide ion size. It therefore seems reasonable to assign the observed transition as the higher energy e-*> a1 transi- tion. On the basis of this assignment it would be predicted that there would be a similar band at lower frequency corn responding to the e —> b1 Singlet—triplet transition. The assignment of the observed band to the e «> a1 transition must be taken as uncertain, at least until the second band is characterized (it is, of course, possible that the second band lies at a higher frequency and is masked by the allowed transitions: the observed band would then be assigned as the e -> b1 transition). D. Infrared Spectra Infrared Spectra in the NaCl Region - The infrared spectrum of the hexamminecobalt(III) ion in the NaCl region has been examined by many workers135 and band assignments have been made106‘109ll35. The Spectrum of hexamminecobalt(III) chloride from 650—2000 cm.-1 is shown in Figure 11 (dashed curve) and the data are given in Table XV. 98 .Ampmaamm umxv HI.Eo Goomlomo coflmmu may GH nosed Umnmmpv moHHoHflo AHHHVHHMQOUmcfiEmemS com Amcfia pHHOmv mumnpmfiao wofluoHSU AHHHVuHmflooHUmCHEEmomUIOUHEmIfl.mo manommm Umumumcfl 0:9 .HH madmflm HI.EU .%ocmoqwum one cow QOOH coma oovH oomH oowH ooom 7 ii. .i ... . 4.. _ . s a, . ’ \ll 4 . ~ ; x x 1 , c _ x 1 z _ 4 x 4 I ~ . x a c c . x 4 / 4 r.. x / 4 , \ / \\ \\ ’1 ‘u I II ‘I\ \‘\\ IIII‘|\\ 99 Table XV. Infrared spectra of some brigged cobalt ammine complexes in the NaCl region (KBr pellets). Co(NH3)6c15 [(NH5)5CONHZCO(NH§)5]CI5c2820 834 (s) 2850 (sh) 720 (w) 1410 (vw) 1330 (s) 2950 (sh) 830 (s) 1623 (s) 1358 (sh) 3150 (s) 1150 vw) 3150 (sh) 1380 (sh) 3250 (s,sh) 1305 m 3230 (s) ( ) ( h ( ( ) 1334 (s) 3430 ( ) [(NH3)5CONH2CO(NH3)5](N03)5 [H20(NH3)4CONH2CoCl(NH3)4]Cl4°4H20 712 (w) 1386 (vs) 825 (m) 1390 (w) 832 (s) 1628 (s) 855 (sh) 1410 (w) 1048 (w) 3170 (sh) 940 (w) 1634 (s) 1300 (sh) 3290 (s) 1108 (w) 3150 (s) 1365 (sh) 1300 (m) 3270 (s) 1330 (s) 3450 (S,b,) [H20(NH3)4CONH2COC1(NH3)4]C14b 824 (S) 3150 (S) 1320 (s) 3210 (s,sh) 1620 (s) aFrequencies in cm.-1; intensities in parenthesis (vs = very strong, 8 = strong, m = medium, w = weak, vw = very weak, sh = shoulder, b = broad). bPrepared by dehydration of the hydrate in vacuo over P205. 100 The bands in the NaCl region are due to vibrations of the ligand in the Co-NHs system (C3V symmetry). The bands may be assigned as follows1°6r1°7r135: the 834 cm."1 band is due to a rocking vibration (pr), the 1330 cm...1 band is due to the Symmetric deformation vibration (08); the band -1. . . . at 1625 cm. is due to the degenerate deformation Vibration (0d), the bands at 3150 and 3250 cm.-1 are the symmetric and assymmetric N-H stretching vibrations (V5 and vas). Diagrams of these vibrations have been given by Nakamotol35. There are, in addition, two shoulders (at 1358 and 1380 cm.-1) on the symmetric deformation band and two shoulders (at about 2850 and 2950 cm.‘1) on the stretching bands. These shoulders might arise because of hydrogen-bonding between the NH3 ligands and the chloride anions, but have thus far resisted characterization. The spectral data for the nitrate and chloride salts of the decammine ion are given in Table XV and the Spectrum of the decammine chloride dihydrate is shown in Figure 11 (solid curve). The decammine nitrate Shows bands character- istic of the free nitrate ion, which have been discussed by Nakamotol36. The assignments of the nitrate ion vibrations .1; — 1048 cm. , :2- 832 cm. , v? _ 1386 cm. 1, and v4 : 712 cm.-1. Since these nitrate bands mask are as follows: some of the characteristic ammine vibrations (particularly Pr and 08), the ammine band positions were determined from the spectrum of the decammine chloride. The spectrum of the decammine chloride dihydrate is 101 shown in Figure 11 and the data are given in Table XV. The bands at 830 cm,._1 and 1623..cm.-1 may be assigned as the ammine rocking (££) and degenerate deformation (0d) vibrations, respectively; the bands in the region 3000-3500 6;.‘1 may be assigned as N-H stretching vibrations; the shoulder at about 3430 cm.-1 is probably due to lattice water137. In the re- gion in which the symmetric deformation (08) vibration is expected, however, three bands now appear—(1305, 1334, and 1378 cm.-1). The assignments for these three bands will be discussed in the next section. The spectrum of the Chloroaquo chloride tetrahydrate is shown in Figure 12, and the data are given in Table XV. The following assignments may be made; the band at 825 cm.‘1 is the ammine rocking Vibration (pr) and the band at 1634 cm.-1 is the ammine degenerate deformation vibration (0d); the two bands at 3150 and 3270 cm.-1 are the N-H stretching vibrations. In addition the broad band at 3450 cm.-1 is probably due to lattice water (O-H stretching vibrations); the shoulder at 855 cm.“1 and the band at 940 cm."1 are probably due to the wagging and rocking vibrations of the coordinated aquo group137. The assignments of the bands at 1108, 1300, and 1330 cm.“1 will be discussed in the next section. It is of interest to note that the spectrum of the anhydrous Chloroaquo chloride (Table XV) (prepared by dehy- dration of the hydrate in vacuo over P205) is quite differ- ent. The bands due to coordinated and lattice water disappear 102 .pmaamm Umumuucmocoo mHOE M MD wms ha Umcflfinmump mm? m>uoo Umflmmp mflu mm GBOSm Esnpoomw one .mumaamm Hmmv HI.EU ooom I Ono COHmmH 0:0 ca ommv.+aomwflmmzvaooo mzoo+flmmzvonmr no 83900006 UmumumcH .NH musmflm H EU .mocmsvmum 0mm cow OOOH OONH OOVH oomfi oowH OOON _ _ _ _ fl _ 103 and the two bands at 1300 and 1330 cm...1 merge to form one band. In addition, the weak band at 1108 cm.-1 apparently disappears. These changes are evidence of both removal of the lattice water and a probable structural change. Far Infrared Spectrum (CsBr Region) of Efamido—decamminedi- cobalt(III) Nitrate - The far infrared Spectrum of the decammine nitrate was determined in a Nujol mull. The data are reported in Table XVI. The Six bands are designated VA through VF in order of decreasing energy; these designations are simply identification labels for use in the discussion of the Spectrum and have no theoretical significance. The assignments of these bands will be discussed in the next section. E. Normal Coordinate Analysis Calculations: Results and Discussion. The normal coordinate analysis calculations were done with the aim of fitting the pattern of the observed spectra for amido-bridged cobalt ammine complexes. The calculations were done separately for the two infrared spectral regions (NaCl and CsBr). (a) The ammine and amido vibrations were analyzed as follows: the pattern of the spectrum of the equatorial ammine system (which corresponds to the Spectrum of the hexamminecobalt(III) ion) was fit- ted with a set of diagonal force constants. A set of force constants was derived from the equatorial 104 Table XVI. Far infrared Spectrum (CsBr region) of Heamido- decamminedicobalt(III) ion (Nujol mull). Frequenc Relativea b cm _1y Intensity Designation 543 w VA 516 w VB 463 w VC 402 m VD 334 s VE 317 sh VF aS = strong, m = medium, w = weak, Sh = shoulder. bThese are identification labels only and have no other significance. 105 system constants for use in the axial system calcu— lations by an approximate adjustment for the dif- ferent Co—N distances. A set of force constants was also derived from the equatorial system con- stants for use in the amido-bridge system calcula- tions. The calculated patterns for the three systems were then used in interpreting the observed infrared spectra in the NaCl region. (b) The decammine ion skeletal vibrations were analyzed by obtaining a set of force constants for the Co-N stretching and N-Co-N bending vibrations of the hexamminecobalt(III) ion and adjusting these con- stants for the decammine ion calculations. The observed spectrum of the decammine ion was then interpreted on the basis of the calculated pattern. The Cobalt-ammine and Amido-bridge Systems - The diagonal force constants derived for the equatorial cobalt-ammine system are shown in the second column of Table XVII. Angle bending force constants are adjusted to the same units (millidynes/R) as the stretching force constants by division by the appropriate equilibrium bond lengths. The vibrational frequencies for the cobalt-ammine system calculated by use of the force constants in Table XVII are given in the third column of Table XIX. Comparison of the data given in Table XIX with the spectral data for Co(NH3)6Cl3 (Table XV, Figure 11) show that the pattern is indeed reproduced (no attempt 106 Table XVII. Force constants for the cobalt—ammine systemsa. Force Constantb Equatorial System Axial System Fr 5.70 5.70 . 2 Fa/rH 0.53 0.53 Fa/rHrCO 0.17 0.20 aForce constants in units of millidynes/R. bDefined in equation (SB-18). Table XVIII. Force constants for the amido-bridge systema Fr = 5.70 millidynes/R F; = 1.00 " Fa/réo = 0.10 " Fé/rfi = 0.53 " Fd/rHrCO = 0.15 aForce constants are defined in equation (SB-19). 107 Table XIX. Results of the normal coordinate analysis calcu- lations for the cobalt-ammine systems.a Vibra— Equatorial . tional Descrip- Co-NH3 From. From Distance- Mode and tionc System(force Equatorial Adjusted Force Symmetry constants Force Constants Species from Constants (Table XVII) Table XVII) S4alb(E) Vas 3248 3248 3248 81 (A1) vs 3138 3138 3138 Ssa’b(E) 8d 1558 1554 1557 53 (A1) as 1437 1362 1391 S6a’b(E) pr 758 700 758 a . . 1 FrequenCies in cm. . bAs defined in Table VIII. Cvas = assymmetric N—H stretch; v = symmetric N-H stretch; s = degenerate deformation; 05 = symmetric deformation; r) o» H O: = rocking. 108 was made to fit the actual frequencies since only diagonal force constants were used.and hydrogen-bonding effects could not be taken into account). Two calculations were then performed for the axial cobalt-ammine system. In the first, the force constants obtained for the equatorial cobalt-ammine system were used unchanged. The calculated frequencies are given in the fourth column of Table XIX. In the second calculation, the force constant for the H-N-Co bending coordinates (Fé) was increased slightly (from 0.17 to 0.20) in order to adjust for the decreased Co-N distance. The new set of force constants is shown in the third column of Table XVII and the calculated frequencies are given in the fifth column of Table XIX. In the above equatorial and axial CObalt— ammine calculations, a value of 1.00 millidynes/g was used for the Co-N stretching force constant (obtained from the hexamminecobalt(III) ion calculations discussed below). Since the Co-N stretching vibration does not affect the am- mine vibrations (because of the large frequency separation), the Co-N stretching frequency is not reported in Table XIX. Vibrations involving Co-N stretching will be discussed below in connection with the decammine ion skeletal vibrations. Two calculations were performed for the amido—bridge system. The first was performed by use of the force con— stants in Table XVIII, but with the H-N-Co bending force constant (Pd) derived from the equatorial system (0.17 milli- dynes/R). In the second calculation, the H-N-Co bending 109 force constant was decreased.(from 0.17 to 0.15) to adjust for the greater Co—N distance (2.2 R).- The calculated fre- quencies for the two calculations are given in Table XX. The value of the Co-N—Co bending force constant (F0) is only approximate. In a study of NH2 deformation frequghcies in polymeric HgNHZCl, Mizushima and Nakagawa138 have used a larger value for the Hg-N-Hg bending force constant (0.100 millidynes/R) than for the H—N-Hg bending force constant (0.089 millidynes/R). In the case of the amido-bridge system, a smaller value was taken for the Co—N—Co bending force constant (0.10 relative to 0.15 millidynes/R for the H-N—Co bending constant) since the bending would actually involve two bulky Co(NH3)5 groups instead of two Co atoms. The observed bands in the spectrum of the decammine ion (Table XVII, Figure 11) may now be assigned on the basis of the results reported in Tables XIX and XX. The bands at 3150 and 3230 cm.-1 in the decammine chloride spectrum may be assigned as the ammine symmetric and assymmetric N-H stretching frequencies, respectively. The data in Table XIX show that the calculated positions of these bands do not change for the closer axial ammine groups. The calcu- lated positions for the amido group N-H stretching fre— quencies (3138 and 3248 cm.-1) fall between the ammine stretching frequencies. Since the ratio NH3:NH2 is 10:1, the intensities of the NH2 stretching vibrations would be expected to be small, so that they are undoubtedly masked by the NH3 stretching bands. 110 Table XX. Results of the normal coordinate analysis calcula- tions for the amido-bridge system . Vibrational From Force Con- From Distance- Mode and . . c stants Derived Adjusted Symmetry Description from Equatorial Force Constants Species Ammine System (Table XVIII) S1 (A1) vaS(N-H) 3228 3227 58 (B2) vS(N-H) 3192 3192 S3 (A1) NHZ bending 1340 1335 S7 (B1) NH2 wagging 1185 1115 95 (A2)e NH2 twisting 1080 1014 S9 (B2) NH2 rocking 345 324 S2 (A1) vS(Co-N) 459 458 S6 (B1) vaS(Co—N) 276 276 S4 (A1) Co—N-Co bending 137 137 a . . 1 FrequenCies in cm. . bAs defined in Table IX. cvas = assymmetric stretch; Vs = symmetric stretch. dForce constants are the same as given in Table XVIII except that Fa/rHrCO - 0.17 millidynes/ . eRaman—active only. 111 The band observed at 1623.cm.-1 should be the combined degenerate deformation vibrations of the equatorial and axial ammine groups, since the calculations for this band (Table XIX) Show that the different Co-N bond lengths do not affect the calculated frequencies significantly. The band at 830 cm.—1 may be the combined rocking vibrations of the equatorial and axial ammine groups. The calculations (Table XIX) show that the position should not change if the distance—adjusted force constants (Table XVII, Column 3) are used: the dis— tance-adjusted force constants are therefore the preferred values for the axial ammine group. The three bands in the region 1300-1400 cm.—1 may be assigned on the basis of the calculated data in Tables XIX and XX and of their relative intensities (see Figure 11). The two more intense bands at 1305 and 1334 cm.“1 may be the symmetric deformation vibration of the axial and ammine groups, respectively. The third band at 1378 cm."1 may be the NHZ bending vibration of the amido group, because of both its low intensity and the calculated data in Table XX. The calculated position for the NHZ bending vibration (using the distance-adjusted force constants) is 1335 cm.-1-lower than the ammine bands. However, the relative intensities might indicate that the higher frequency band is due to NH2 bending vibration; therefore, the force constants in Table XVIII should be regarded as only approximate. The results in Table XX Show that the NHZ wagging vibra- tion should be found in the region 1100-1200 cm._1. Since no such band is seen in Figure 11, the spectrum of the 112 decammine chloride was determined by use of a highly concen- trated KBr pellet. A very weak band was observed at 1150 -1 . . . cm. . This band may be tentatively aSSigned as the NHZ wagging vibration. The reason for the extremely low intensity is unclear if the assignment is correct. The Chloroaquo ion also gives a weak band in the same region (1108 cm.-1, see Table XV, and Figure 12) and may support the above assign- ment. The weak band at 1150 cm...1 might,however, have a different cause (such as overtones). The concentrated KBr pellet also showed two other weak bands at 720 and 1410 cm.-1. The origin of these bands is not clear and might be associated with hydrogen-bonding ef- fects. Indeed, the band at 1378 cm._1, assigned as the NH2 bending vibration, may also be due to hydrogen-bonding of the ammine groups. The bands at 1378 and 1410 cm.-1 may be Similar to the shoulders observed for the hexamminecobalt(III) ion at 1358 and 1380 cm.“1 and may be attributed to the same (unknown) cause; the NHZ bending vibration may be as weak as the wagging vibration (at 1150 cm.—1) and therefore may be masked by the ammine 05 bands. Thus, although the bands at 1378 and 1150 cm.-1 are assigned as the NH2 bending and wagging vibrations, those assignments must remain tentative. The other amido group vibrations indicated in Table XX were not observed. The NHZ twisting vibration is not infra— red active, and was therefore not observed. The NH2 rocking and Co-N stretching vibrations would actually involve skele— tal Vibrations; therefore the calculated frequencies are 113 meaningless. The skeletal vibrations will be discussed below. The Co-N-Co bending vibration would be expected to lie below 200 cm.-1; since the force constants are only approximate, the calculated frequency (137 cm.-1) is also approximate. The spectrum of the decammine ion was not determined below 200 cm.-1. The spectrum of the Chloroaquo chloride (Table XV and Figure 12) may be interpreted in a similar manner. The bands at 1300 and 1330 cm.-1 may be the symmetric deformation vibration of the axial and equatorial ammine groups, respec- tively. The weak bands at 1390 and 1108 cm._1 may be ten- tatively assigned as the NHz bending and wagging vibrations. As in the decammine spectrum, the NHZ bending and wagging assignments are only tentative because of the low intensi- ties. The weak band at 1410 cm.-1 is similar to the 1410 cm.-1 band in the decammine spectrum and might also have its origin in hydrogen-bonding. The other bands (and shoulders) in the Chloroaquo ion spectrum have been discussed in the preceding Section (VID). The Skeletal Vibrations of the_pramido-decamminedicobalt(III) .123 - The force constants used in the normal coordinate analysis calculations for the decammine ion skeletal vibra- tions were derived from an approximate set of force constants calculated for the hexamminecobalt(III) ion.‘ The force constants for the hexamminecobalt(III) ion were determined to match the observed spectrum. There is, however, much 114, dispute in the literature over the far infrared spectrum of the hexamminecobalt(III) ion. Block108 reported only a band at 490 cm.-1, which he attributed to the assymmetric cobalt- Initrogen stretching frequency. Blyholder and Ford47 observed a weak band at 502 cm.-1 and a strong band at 330 cm.“1 Nakamotollo reported bands at 500, 476, 448, and 327 cm.-1, and assigned the first three bands to the Co-N stretching vibration (Split by the crystal field) and the last band to the N-Co-N bending vibration. Shimanouchi and Nakagawa109 observed a strong band at about 320 cm.-1. In addition, they observed some very weak bands at higher frequencies (585 cm.-1 for the bromide and iodide salts and 503 and 492 cm.-1 for the bromide salt). Their assignments agree with those of Nakamotollo. In Spite of the conflicting reports, the hexammine- cobalt(III) ion spectrum certainly has a weak band at about 500 cm...1 and a strong band at 320-330 cm.-1. In the present investigation, this pattern was matched in a normal coordinm ate analysis calculation by use of the following force constants: Fr = 1.00 millidynes/R FO/r§ = 0.48 miliidynes/R (6Ee1) Frr, = 0.05 miliidynes/R where Fr is the Co—N stretching force constant, F0 is the N-Co-N bending force constant and Frr' is the bond stretch- ing interaction constant (see equation (20), Section VB). The fundamental frequencies of the hexamminecobalt(III) ion 115 calculated from these.constants (equation (1)) are: -1 v1(A1g) = 353 cm. v2(Eg) = 308 " V3(T1u) = 511 " (6E-1) v4(T1u) = 308 " v5 (T29) = 438 " V6(T2u) 3 309 " . Diagrams of these vibrations have been given by Nakamotol39. The two T1u frequencies (511 and 308 cm.-1) correspond to the two bands observed in the spectrum. The calculated pattern also agrees with the calculations of Shimanouchi and Nakagawa109. The force constants for the decammine ion calculation were derived from the hexamminecobalt(III) ion diagonal force constants (Fr and F0) by an approximate adjustment for the different bond lengths. The values of the decammine ion force constants used in the calculation are given in Table XXI. The force constants have been defined in equation (SB-22). The results of the calculation for the decammine ion skeletal vibrations are given in Table XXII. The calcu— lated frequencies are given in the second column. Only the eight A and Eu vibrations (v1 through v8) are infrared 2u active: the A B , B and E vibrations (v9 through 19' 19 29' 9 __ v19) are Raman active. The nature of each vibration is given in the third column as a linear combination of the 116 Table XXI. Force constants for the skeletal vibrations of the Efamido-decamminedicobalt(III) ion F; = 1.00 miliidynes/R Fa = 1.25 " I‘ b F — 0.85 " r e F /r2 — 0.48 " 0 e Fa/r r = 0.53 " 0 ea b _ . Fa/rerb 0.45 aForce constants are defined in equation (SB-22). 117 Table XXII. Results of.the normal coordinate analysis calcu- “lations for the skeletal vibratigns of the E? amido—decamminedicobalt(III) ion . Speciesb Calculated Distribution of the vibration and Frequency, Among the Symmetry Coordinates ’ Activity cm.-1 A2u(IR) 536 (v1) 0.5982 - 0.6183 - 0.5384 404 (v2) 0.5282 + 0.8083 - 0.3084 338 (v3) 0.89s2 - 0.0983 + 0.4584 316 (v4) S1 f Eu(IR) 544 (v5) 0.6285a+0.1085b-0.34S6a+0.25s6b -0.35S7a—0.06SSb-0.5458a-0.09S8b 497 (v6) 0.2585a-0.0185b-0.1286a+0.1286b _ + _ 0.7187a 0.02S7b+0.64s8a 0.0188b 355 (v7) 0.6385a+0.22S5b-0.35S6a+0.17S6b +0.53S7a+0.18S7b+0.29S8a+0.1088b 312 (v8) 0'7955a+0'0285b+0’44s6a-0'4286b -0.0287a+0.00S7b-0.01S8a-0.0088b A1g(R) 509 (v9) 0.73s10 - 0.26s11 - 0.64s12 340 (v10) -0.92Slo — 0.05811 - 0.40812 316 (v11) 89 97 (v12) 0.12810 + 0.98811 - 0.18512 B1g(R) 316 (v13) 813 304 (v14) $14 B2g(R) 438 (v15) $15 118 Table XXI. (Continued) Speciesb Calculated Distribution of the Vibration d e and. a Frequency, Among the Symmetry Coordinates ’ ActiVity cm.‘ Eg(R)f 526 (V16) -0.66sl6a-0.05816b+0.34sl7a-0.29817b +0°595183+0'05818b+0°llsl9a+0.01819b 409 (017) -0.50516a—0.17816b+0.31S17a-0.28817b ‘0'64518a-0'22818b+0'35819a+0“12819b 313 (V18) 0.78516a+0,23516b+0.51S17a--0.28S17b _0.00318a_0.00518b+0.02S19a+0.00S19b 214 (v19) 0,28316a—0.24S16b—0.02817a+0.27s17b +0.19S18a-0.16818b+0.64819a-0.66S19b B u(1) 438 (v20) 820 B u(I) 316 (V21) 821 304 (v22) 822 aThe force constants in Table XXI were USGd- bFor D4h symmetrY- CIR = infrared active; R = Raman active; I = inactive. dThe symmetry coordinates are defined in Table X. eThe coefficients are the normalized elements of the L ‘1 matrix (the inverse of the eigenvector matrix). f (Eu Only one linear combination is given for the degenerate and E9) vibrations. 119 symmetry coordinates defined in Table X. The coefficients of the symmetry coordinates were obtained by normalizing the rows of the inverse of the eigen-vector matrix (i.e. the Lil matrix). Only one linear combination is given for each of the degenerate vibrations (the Eu and Eg vibrations): the other combination may be obtained simply by reversing the coefficients of each set of degenerate symmetry coordin- ates. The molecular motions involved in the infrared active A2u and Eu vibrations are shown schematically in Figure 13. The vectors in the diagrams indicate only the relative di— rections of the atomic motions, but not the relative magni- tudes. The magnitude of the cobalt atom motions will of course be much smaller than ammine group motions. The cor- responding symmetric Alg and Eg motions may be obtained simply be reversing the directions of the vectors on one side of the molecule. The symmetric B1g and B29 motions may be easily obtained by inspection of the correSponding sym— metry coordinates. Since only the infrared spectrum of the decammine ion was determined in this investigation, only the infrared active A2u and Eu vibrations will be discussed. The v1, :2} and v3 Vibrations (AZu) differ only in the direction of motion of the cobalt atoms and axial ammine groups relative to the motion of the equatorial ammine groups. In the v2 vibration, all the atoms move in the same direc- tion while in v1 the cobalt atom motions are the opposite of the ammine group motions. In vs, the axial ammine group Figure 13. 60 <~o eo <—o eoo—> «00230 60 60 <—o e0 e0 eo 606.0690 *0 eo *0 “O o—> 0+ 0+ 600 03w o—> o—> m o» C>9 OKOOONO Q5 0 3? Schematic diagrams of the A ‘3 b O 120 6 8 <5 V5(Eu) 8 633 O £6 (5 <3 8 3635 0 $3336 6 v6(Eu) 6 6 8 v (E ) 5; 61‘ 7 u (2 C O 56 66? 6 3 V8(Eu) C 9. O 9“ C a? 559 and E skeletal vibration of the Eramido-deggmminedicobalt(III) ion. motion is shown. atoms, the Open circles are nitrogen atoms. Only one of each set of degenerate E The dark circles are cob lt 121 motions are opposite the equatorial ammine motions - the co- balt atoms remain stationary. The v4 vibration is a.pure assymmetric stretch and involves no angle deformation. The Eu vibrations v5, v6, and v7 also differ only in the relative directions of the atomic motions. In V6 all the atoms move in the same direction, in v5 the cobalt atom motions oppose the ammine group motions and in v7 the axial ammine group motions Oppose the equatorial ammine and cobalt atom motions. The V8 vibration involves only equatorial ammine group motions. A comparison of the calculated frequencies of the A2U and Eu vibrations from Table XXII with the observed spectrum (Table XVI) shows that the pattern of the observed spectrum has been reproduced in the calculations. The three high frequency bands VA, VB, and VC (see Table XXVI) should be the v5, v1, and v6 vibrations (see Table XXII) respectively. The VD band (at 402 cm.—1) may be the v2 vibration. The observed band at 334 cm.—1 (v ) is very broad and includes 1 .__ the shoulder at 317 cm.- ( ). The v band (including v ) E F it. may then be the sum of the v3, v4, v7, and v8 vibrations. Lowering the symmetry to C2v (the bent structure deter- mined by Vannerberg20 and shown in Figure 1) would cause the I B . B to become infrared 4h 1g 1g 2g’ 2u active. The corresponding bands are not observed experimental- D vibrations A Eg and B ly, so that the decammine ion apparently acts as a complex with D4h symmetry in the far infrared region. This conclusion 122. is in accord with the results of the fig calculations and the electronic spectrum of the decammine ion. The three internal coordinates that were neglected in the calculation - two linear valence angle bending coordinates (Eu) and a torsional (Alu) coordinate - are of little con— sequence. The torsional coordinate (twisting of the two halves of the ion in opposite directions) is not infrared active in either D or C 4h 2v angle bending coordinates actually correspond to the Co-N symmetry. The two linear valence b-Co bending vibration. This vibration has been discussed in Con- nection with the amido-bridge system and is expected to lie below 200 cm.—{ It is significant that the pattern of the observed spectrum of the decammine ion could be reproduced by use of the force constants in Table XXI. The differences in the values of the different stretching and bending force constants reflect only the differences in the bond lengths. The three different cobalt-nitrogen bonds (Co-Ne, Co-Na, and Co-Nb) in the decammine ion are thus electronically very similar. This conclusion agrees with the results of the g9_calcula- tions which indicate that the three types of bonds are all essentially gfbonds and that w—bonding contributes very little to the Co-N bond stability. 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