Preface to the title at left, 1962 I have tried to give an introduction to that field of chemistry which deals with the spectral and magnetic features of inorganic complexes. It has been my intention not to follow the theory in all its manifestations but merely to describe the basic ideas and applications. This has been done with an eye constantly aimed at the practical and experimental features of the chemistry of the complex ions. The book is thus primarily intended for the inorganic chemist, but it is true that, in order to follow the exposition, a course in basic quantum mechanics is needed. Simple examples are nearly always used to illustrate the arguments, but the quoted experimental evidence must of necessity be limited. Nevertheless, in the last chapter an attempt has been made to cover most of the important work so far performed that lies within the scope of the book. However, the field is advancing so rapidly that a complete survey would be outdated before long.

Since I am a chemist writing for chemists, my emphasis and notation will probably appear clumsy to the physicists primarily responsible for the theory. For this I make no excuse. Elegant derivations and condensed notation are in my opinion not desirable in an introduction to a field.

Nothing is more dangerous than to force every observation into a fixed framework of ideas. I have tried to present the case for the ligand field theory as it is now understood. It is my personal view that there are really only a few places where we need to revise part of the theory in order to understand the sundry phenomena. It must always be remembered, however, that the ligand field theory offers only a model of nature, with all the inherent limitations of models.

I want particularly to thank, among many others, Dr. Andrew D. Liehr, Mellon Institute, Dr. Max Wolfsberg, Brookhaven National Laboratories, and Dr. Harry B. Gray, Columbia University, for numerous discussions and for help with the manuscript. I am also greatly indebted to Mrs. Lise Seifert for her assistance in preparing the manuscript. Finally, I want to thank the editors of Annual Review of Physical Chemistry for permission to draw from the 1956 paper written by the late Prof. W. Moffitt and myself.

                             Carl J. Ballhausen

 


                                     Contents
         
         
         Preface  .....................................................     V   
                                          

         Chapter 1  INTRODUCTION .....................................       1

                  1-a.  History of complexes ..........................      1
                  1-b.  Theories of bonding ...........................      2
                  1-c.  History of the crystal field approach .........      3
                   References .........................................      5


         Chapter 2  THEORY OF ATOMIC SPECTRA ..........................      7

                  2-a. Orbitals and states ............................      7
                  2-b. Atomic wavefunctions ...........................     10
                  2-c. The raising and lowering operators .............     11
                  2-d. Matrix elements ................................     15
                  2-e. Two-electron operators .........................     17
                  2-f. Evaluation, matrix elements (ab|1/r12|cd) .......    19
                  2-g. Term energies ..................................     21
                  2-h. General remarks on the method ..................     25
                  2-i. Spin-orbit coupling in a hydrogen-like system ..     25
                  2-j. Spin-orbit coupling in a many-electron case ....     27
                  2-k. Absolute term intervals ........................     29
                  2-l. Zeeman splitting ...............................     30
                  2-m. Selection rules ................................     32
                  References ..........................................     33


         Chapter 3   SYMMETRY .........................................     34

                 3-a. Concept of symmetry operators ...................     34
                 3-5. Nomenclature of symmetry operators ..............     36
                 3-c. Representations .................................     37
                 3-d. Important point groups in inorganic complexes ...     41
                 3-e. Representations and wave functions ..............     43
                 3-f. The direct product ..............................     46
                 3-g. Double groups ...................................     49
                 3-h. The Eulerian angles  ............................     54
                References ............................................     56


         Chapter 4  THE CRYSTAL FIELD THEORY: I. FIELDS OF OCTAHEDRAL
                    SYMMETRY ..........................................     57

                4-a. Formalism  .......................................     57                            
                4-b. Octahedrai fields ................................     60
                4-c. Single d electron in a cubic field ...............     62
                4-d. Weak fields ......................................     69
                4-e. Strong fields ....................................     74
                4-f. Fields of intermediate strength ..................     80
                4-g. Computation aids .................................     84
                4-h. Descent in symmetry ..............................     87
                4-i. Equivalence of t2g and p electrons ................     89
                4-j. The spectrochemical series .......................     91
                Appendix 1 ............................................     93                                         
                Appendix 2 ............................................     95                                               
                Appendix 3 ............................................     96
                References ............................................     97


         Chapter 5   THE CRYSTAL FISLD THEORY: II. FIELDS OF TETRAHEDRAL
                     AND OF LOWER SYMMETRY  ...........................     99

                5-a. Tetragonal fields ................................     99
                5-b. Trigonal fields ..................................    103
                5-c. Cis, trans and rhombic fields ....................    106
                5-d. Tetrahedral fields ...............................    108
                Appendix l ............................................    111
                References ............................................    112


         Chapter 6  SPIN-ORBIT COUPLING ...............................    113

                6-a. Importance of spin-orbit coupling ................    113
                6-b. Spin-orbit coupling,one d electron, octah. fields     114
                6-c. Spin-orbit coupl.,dn-config.,oct. fields   120
                6-d. Spin-orbit split. calc., method Abragam & Pryce ..    124
                6-e. g factors in an octahedral field .................    127
                6-f. g factors in a tetragonal or trigonal field ......    131
                6-g. The spin Hamiltonian .............................    137
                6-h. Magnetic susceptibilities ........................    139
                Appendix 1 ............................................    149
                Appendix 2 ............................................    149
                References ............................................    150


         Chapter 7  MOLECULAR ORBITALS ................................    152

                7-a. General discussion................................    152 
                7-b. Bonding scheme for an octahedral complex .........    159
                7-c. Estimation of wave functions in an MO acheme .....    163
                7-d. Band intensities in parity allowed transitions ...    170
                Appendix 1 ............................................    174
                Appendix 2 ............................................    177
                References ............................................    178


         Chapter 8   VIBRONIC INTERACTIONS ............................    180

                8-a. Vibrational spectra ..............................    180
                8-5. Absorption band intens., centrosymmetric complexes    185
                8-c. Dichroism ........................................    192
                8-d. Jahn-Teller configurational instabilit ...........    193
                8-e. Experimental Evidence of the Jahn-Teller Effect ..    205
                References ............................................    208


         Chapter 9  SOME FURTHER ASPECTS ..............................    211

                9-a. The Faraday effect ...............................    211
                9-b. Optical rotatory dispersion ......................    214
                9-c. "Sandwich" compounds .............................    217
                9-d. Stability of complex ions ........................    221
                References ............................................    224


     Chapter 10  ELECTRONIC STRUCTURES OF SELECTED INORGANIC
                 COMPLEXES ............................................    226 

                Complexes Containing 3d Electrons .....................    227  VIEW !
        
               10-a.    Scandium ......................................    227   
               10-b.    Titanium ......................................    227             
               10-c.    Vanadium ......................................    228           
               1O-d.    Chromium ......................................    235       
               10-e.    Manganese  ....................................    245         
               10-f.    Iron ..........................................    251         
               10-g.    Cobalt ........................................    255     
               10-h.    Nickel ........................................    261    
               10-i.    Copper ........................................    268    
         
                Complexes Containing 4d and 5d Electrons ..............    273 
         
               10-j.    Niobium .......................................    273              
               10-k.    Molybdenum ....................................    274         
               10-1.    Technetium ....................................    275
               10-m.    Ruthenium .....................................    275        
               10-n.    Rhodium .......................................    276      
               10-o.    Palladium .....................................    277      
               lO-p.    Tungsten ......................................    277   
               10-q.    Rhenium .......................................    278 
               10-r.    Osmium ........................................    279
               10-s.    Iridium .......................................    281     
               10-t.    Platinum ......................................    282         
               References .............................................    283
         
         Index  .......................................................    293