Matrix Operator Output (MATRIX) Keyword

• Notes
  The MATRIX keyword provides a powerful utility for obtaining general matrix elements of chosen operators (OP) or basis set (BAS) transformations of interest. The particular choice of matrix is specified by two entries of a bracket-list that follow the MATRIX keyword.

  To specify a chosen operator matrix for a chosen operator OP in a chosen basis BAS, the input form is

  MATRIX <OP/BAS>

  For example, "MATRIX <FOCK/NBO>" specifies the Fock (or Kohn-Sham) matrix in the NBO basis, whereas "MATRIX <KINETIC/PNLMO>" specifies the kinetic energy matrix in the PNLMO basis.

  To specify a chosen transformation matrix from one basis (BAS1) to another (BAS2), the input form is

  MATRIX <BAS1/BAS2>

  For example, "MATRIX <AO/MO>" specifies the LCAO-MO transformation from basis AOs to MOs, whereas "MATRIX <NAO/NLMO>" specifies the LCNAO-NLMO transformation from NAOs to NLMOs.

  In the above commands the chosen BAS name may be chosen from any of the twelve recognized basis sets:

  BAS: AO, NAO, NHO, NBO, NLMO, MO, NO, PNAO, PNHO, PNBO, PNLMO, PAO

  The chosen OP name may be chosen from any 1e operator included in the input archive (.gen) file, such as

  • "DM" or "Density" (density operator),
  • "S" or "Overlap" (unit operator),
  • "F" or "Fock" (Fock/Kohn-Sham operator),
  • "K" or "Kinetic" (kinetic energy operator),
  • "V" or "Nuclear" (nuclear-electronic potential),
  • "DI" or "Dipole" (electric dipole moment)

  In addition, the SD (spin-density) operator is available for all open-shell NBO options.

  Alternatively, OP might be any operator provided to NBO from the host ESS program through general ESS/NBO message-passing protocol. Check the ESS User Manual for valid OP options available in your host ESS program. Symbolic names or abbreviations for OP or BAS entries are generally case-insensitive.

  A single MATRIX keyword may be followed by multiple (up to 25) bracket lists for different matrices, such as

  MATRIX <S/PNBO> <DIPOLE/NLMO> <NAO/NO>

  "Old-style" keywords such as SPNBO or DINLMO are still recognized for some of these options, but many new possibilities become available in NBO 6.

  The sample Gaussian I/O below illustrates requests for the Fock matrix in the NBO basis ("matrix <fock/nbo>") and the AO → NAO transformation matrix ("matrix <ao/nao>") for formamide. In each case the output format is similar to that for the respective "old-style" keywords FNBO, AONAO (which are still recognized in NBO 6).

• Sample Input
  
  #rhf/3-21g pop=nboread
  
  RHF/3-21G for idealized methylamine
  
  0 1
  C
  N  1  1.47
  H  1  1.09  2   109.4712
  H  1  1.09  2   109.4712  3  120.
  H  1  1.09  2   109.4712  3 -120.
  H  2  1.01  1   109.4712  4  180.
  H  2  1.01  1   109.4712  5  180.
  
  $nbo matrix <fock/nbo> <ao/nao> $end
  
  

• MATRIX Sample Output
  

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