关键词：键级，Mayer键级

一般性参数设置（参数参考：单点能计算、HOMO、LUMO、IP、EA的计算、分子轨道的成分）

计算完毕后，得到所有原子，两两之间的MAYER、G-J、N-M (1)、N-M (2)、N-M (3) (*)键级关系：

 B O N D - O R D E R  A N A L Y S I S
 
 
 
 
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                          DIST. [A]                   BOND-ORDERS
                                                  (THRESHOLD =  0.200 )
 -----------------------------------------------------------------------------------------------
                                      MAYER        G-J    N-M (1)    N-M (2)    N-M (3) (*)
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  O      1 - H      2     0.9600     1.0086     0.8599     1.1959     1.2719     1.1962
  O      1 - H      3     0.9600     1.0088     0.8600     1.1960     1.2719     1.1963
 -----------------------------------------------------------------------------------------------
 Sum :                               2.0330     1.7213     2.3935     2.3935     2.3935
 -----------------------------------------------------------------------------------------------
 Atomic summation :
 -----------------------------------------------------------------------------------------------
  O      1                           2.0174     1.7199     2.3919     2.5437     2.3925
  H      2                           1.0242     0.8612     1.1975     1.1216     1.1972
  H      3                           1.0245     0.8613     1.1976     1.1216     1.1973
 -----------------------------------------------------------------------------------------------
 
 (*) Values from: 
     - Mayer bond-order analysis
     - Gophinatan-Jug bond order analysis
     - Nalewajski-Mrozek bond order analysis
       a) N-M (1) - bond-orders calculated from two-electron valence indices
                         based on partitioning of tr(Delta_P^2] (3-index set)
       b) N-M (2) - bond-orders calculated from two-electron valence indices
                         based on partitioning of tr(Delta_P^2] (4-index set)
       c) N-M (3) - bond-orders calculated from valence indices
                         based on partitioning of tr(P*Delta_P] 
      A. Michalak, R.L. DeKock, T. Ziegler, J. Comp. Chem., subm.
      and original articles by Nalewajski et al. )
 Mulliken charges used for AMS results%charges...

N-M(i)指Nalewajski-Mrozek键级的不同版本，G-J指Gopinathan-Jug键级。

N-M键级的定义，参考文献：

• R.F. Nalewajski, J. Mrozek and A. Michalak, Two-electron valence indices from the Kohn-Sham orbitals, International Journal of Quantum Chemistry 61, 589 (1997)
• M. Mitoraj, A. Michalak and T. Ziegler, A Combined Charge and Energy Decomposition Scheme for Bond Analysis, Journal of Chemical Theory and Computation 5, 962 (2009)
• R.F. Nalewajski and J. Mrozek, Modified valence indices from the two-particle density matrix, International Journal of Quantum Chemistry 51, 187 (1994)
• R.F. Nalewajski, J. Mrozek and A. Michalak, Exploring Bonding Patterns of Molecular Systems Using Quantum Mechanical Bond Multiplicities, Polish Journal of Chemistry 72, 1779 (1998)
• R.F. Nalewajski, J. Mrozek and G. Mazur, Quantum chemical valence indices from the one-determinantal difference approach, Canadian Journal of Chemistry 74, 1121 (1996)

G-J键级的定义，参考文献：

• M.S. Gopinathan and K. Jug, Valency. I. A quantum chemical definition and properties, Theoretica Chimica Acta 1983 63, 497 (1983)

Mayer键级的定义，参考文献：

• I. Mayer, Charge, bond order and valence in the ab inition SCF theory, Chemical Physics Letters 97, 270 (1983)