Natural Bond-Bond Polarizability Indices (NBBP)
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References
H. E. Zimmerman and F. Weinhold, J. Am. Chem. Soc. 116, 1579-1580 (1994); J. Org. Chem. 78, 1844-1850 (2013);
C. A. Coulson and H. C. Longuet-Higgins, Proc. Roy. Soc., A191, 39 (1947); A192, 16 (1947).
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Notes
The natural bond-bond polarizability (NBBP) is closely related to the original BBP index of Coulson and Longuet-Higgins, but is computed with ab initio Fock or Kohn-Sham matrix elements between bonding NHOs. Formally, the NBBP index B(b;b') = B(r,s;t,u) for bonds b, b' (associated with bonding hybrids r, s for bond b and t, u for bond b') is the 2nd-derivative of energy E with respect to NHO Fock matrix interaction elements Fr,s, Ft,u of the two bonds, indicative of how a perturbation of one bond will affect the other through conjugative or hyperconjugative couplings. The NBBP indices for all NBOs of the natural Lewis structure are printed by default (keyword NBBP), but other keyword options allow one to obtain these indices for any possible (bonded or non-bonded) hybrid indices. Results are illustrated for the formamide molecule, RHF/3-21G level at B3LYP/6-311++G** geometry (see NBO 6.0 Manual, p. B97-99 for additional discussion).
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Sample Input (G9X)
#rhf/3-21g pop=nboread
RHF/3-21G for formamide (H2NCHO)
0 1
H -1.908544 0.420906 0.000111
H -1.188060 -1.161135 0.000063
N -1.084526 -0.157315 0.000032
C 0.163001 0.386691 -0.000154
O 1.196265 -0.246372 0.000051
H 0.140159 1.492269 0.000126
$nbo nbbp $end