Wave-function: Match

See examples in MatchMO.mw

Procedures

• MatchMO(A1,A2,moS1,mo2,minO,output,/lsi,KKB,{sym,ev,S,maxdS,maxrot,det:=1,printout,printO,raiseerror}) match two sets of MOs where
  • moS1::Matrix(n1,N1),mo2::Matrix(N2,n2) are orbitals to match,
  • minO::numeric discard matched pairs with smaller O12[o1,o2],
  • output::string sequence of character-codes, see below,
  • lsi::[lsi1,lsi2::list(posint)]:=[[]$2] subset of atoms for each molecule used in matching,
  • KKB::{[K1,K2::list(posint),BS2],[BS1,BS2],[BS2]}:=[] defines subset of basis set indexes |K1|=|K2|=N used in matching, here K1,2 are the subset of indexes and BS1,2 are the basis sets; note that only BS[k][1]=i mapping is used to derive K from lsi, but entire BS2 is used for MO2 rotation,
  • sym::list:=[sym1,sym2::{list,Vector}(string),/w]:=[] MO-symmetries, if w>0 it is the penalty for symmetry mismatch in matching MOs,
  • ev::list:=[ev1,ev2::Vector,/de] MO-energies, if de>0 then ((ev1-ev2)/de)^2 is the penalty for energy mismatch in matching MOs,
  • S::[S1,S2]:=[] basis set overlaps, if provided then moS1 must be mo
  • maxdS::numeric:=1e-8 threshold for |S1-S2| to use S12=sqrt(S1[K1,K1]).sqrt(S2[K2,K2]) instead of S1[K1,K1],
  • maxrot::numeric:=0.1 threshold for |R-1| to rotate MO2,
  • det::{-1,0,1}:=1 passed to Superimpose command,
  • printout::{boolean,posint}:=false number of smallest-overlap orbitals to print (default is 9),
  • printO::nonnegint:=0 size of O12 submatrix to print,
  • raiseerror raise error if there are unmatched MO1.
  Output codes:
  • a superimposed A2,
  • b derived basis set overlap matrix S12::Matrix(N),
  • d RMSD deviation in geometry,
  • e permuted ev21::Vector(n1),
  • m permuted and sign-corrected mo21::Matrix(N2,n1),
  • o overlap matrix O21::Matrix(n1) between MOs1 and rotated and matched MOs2,
  • q overlap matrix O12::Matrix(n1,n2) between MOs1 and rotated MOs2,
  • p permutation P21::list(n1) of MOs2, so that e.g. ev21=ev2[P21] except for unmatched MOs1 for which P21[o]=0,
  • r rotation matrix A2 to A1,
  • s correction signs for MOs2 after permutation s21::Vector(n1),
  • u number of unmatched MOs1,
  • v list of [o1,o2,val[o1,o2],O12[o1,o2],ev2[o2]-ev1[o1],[ev1[o1],ev2[o2]],[sym1[o1],sym2[o2]]] for matched orbitals sorted by o1,
  • y permuted sym21::Vector(n1),
  • 1 subset K1
  • 2 subset K2
  Notes:
  • MOs are matched using IdentifyPairs by val[o1,o2]=-O12[o1,o2]^2 plus symmetry and energy penalties as described above.
  • The command tries to match all MOs1, so that the output entries corresponding to unmatched MOs1 are all set to zero or empty string.
  • Both lsi1,2 and K1,2 should be taken large enough to represent MOs of interest.