Natural Cluster Unit (NCU) Analysis

• Reference
  E.D. Glendening, C. R. Landis, and F. Weinhold, J. Comp. Chem. 34, 1429-1437, 2134 (2013)
  
  

• Notes
  The Natural Cluster Unit (NCU) keyword launches a search for evidence of interatomic clustering patterns, both above and below the threshold for "molecular" cluster formation. The NCU search seeks to identify each new "natural cluster unit" (a particular collection of atoms, labelled by {C}) as the search threshold t_C is progressively lowered from high values (where only free atoms survive) to low values (where all atoms belong to the sole remaining "unit"). The t_C value therefore serves as a type of characteristic "temperature" for formation of cluster C, with higher t_C values corresponding to complete dissociation to free atoms and lower values corresponding to progressive molecular and supramolecular aggregation.

  Interatomic elements of the DMNAO density matrix are employed as intrinsic measures of apparent A--B interaction strength s_AB, evaluated as the norm (Tr{D*D}^1/2) of the NAO density matrix block between atoms A and B. Atoms A, B are considered to be "linked" for threshold values below this magnitude (t_C ≤ s_AB). A natural cluster unit {C} at threshold t_C consists of all atoms having contiguous linkage(s) (s_AB ≥ t_C) with other atoms of the common aggregation unit. The NCU search varies t_C within a user-selected range and granularity (t_min, t_max, Δt) of threshold values, specified by keyword parameters of the form

  NCU=t_min,t_max,Δt

  If only a single parameter value is assigned (e.g., "ncu=0.15"), the natural cluster units are returned for this single value of t_C. If no parameters are included, the search defaults to t_min = 0.1, t_max = 1.0, Δt = 0.01.

  NCU keyword usage is illustrated below for a model water dimer at RHF/6-311++G** level , showing successive aggregation into ionic, molecular, and supramolecular cluster units as the cluster interaction threshold t_C is lowered. (See NBO 6.0 Manual, pp. B?-? for additional discussion).

• Sample Gaussian Input
  
  %chk=h2o_h2o
  #N rhf/6-311++G** POP=NBORead
  
  H2O...HOH
  
  0 1
  H   0.036726   0.556520   0.000000
  O  -0.006183   1.525447   0.000000
  H   0.909465   1.817564   0.000000
  O  -0.006183  -1.376675   0.000000
  H  -0.423629  -1.782131   0.767110
  H  -0.423629  -1.782131  -0.767110
  
  $NBO ncu $END
  
  

• Sample Output
  

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