Finally, and as any other method for use in empirical modeling of experimental
data, conformational averaging has to be performed whenever there exists more
than one thermally-accessible rotamer that compete significantly for the molecular
population as governed by the Boltzman-distribution at the temperature of interest.
3.3 The Electron Density-Weighted Adjacency/Connectivity
Matrix (EDWAM/EDWCM)
The LDM requires for its determination a quantum chemical calculation since the
calculation of the LIs and DIs requires the electron density and the electron pair
density contained in the second order density matrix which is inaccessible from
experiment [29].
The usage of matrix representatives of molecules is not restricted to LDMs and
can be extended to quantities directly derivable from both theory and experiment
such as the matrix of Coulombic nuclear-nuclear repulsion, the distance matrix, or
the matrices of bond critical point (BCP) properties such as the electron
density-weighted adjacency/connectivity matrix (EDWAM/EDWCM) [22–24, 30].
The chemical graph theoretic hydrogen-suppressed connectivity matrix of ethane
is:
ð3:22Þ
with a determinant of −1, a vector D = (1, −1), and the characteristic polynomial:
k
2
À 1:
ð3:23Þ
The unique features and properties of this molecule are captured with a higher
fidelity and specificity if (a) the “ones” in the above matrix are multiplied
(weighted) by the value of the electron density (in a.u.) at the bond critical point
(BCP), and (b) if all atoms are kept including hydrogen atoms to yield an EDWAM
representative of this molecule. The idea of EDWAM was first communicated
to one of us (CM) by Professor Lou Massa in the form of a private communication
[30].
66
C.F. Matta et al.
data, conformational averaging has to be performed whenever there exists more
than one thermally-accessible rotamer that compete significantly for the molecular
population as governed by the Boltzman-distribution at the temperature of interest.
3.3 The Electron Density-Weighted Adjacency/Connectivity
Matrix (EDWAM/EDWCM)
The LDM requires for its determination a quantum chemical calculation since the
calculation of the LIs and DIs requires the electron density and the electron pair
density contained in the second order density matrix which is inaccessible from
experiment [29].
The usage of matrix representatives of molecules is not restricted to LDMs and
can be extended to quantities directly derivable from both theory and experiment
such as the matrix of Coulombic nuclear-nuclear repulsion, the distance matrix, or
the matrices of bond critical point (BCP) properties such as the electron
density-weighted adjacency/connectivity matrix (EDWAM/EDWCM) [22–24, 30].
The chemical graph theoretic hydrogen-suppressed connectivity matrix of ethane
is:
ð3:22Þ
with a determinant of −1, a vector D = (1, −1), and the characteristic polynomial:
k
2
À 1:
ð3:23Þ
The unique features and properties of this molecule are captured with a higher
fidelity and specificity if (a) the “ones” in the above matrix are multiplied
(weighted) by the value of the electron density (in a.u.) at the bond critical point
(BCP), and (b) if all atoms are kept including hydrogen atoms to yield an EDWAM
representative of this molecule. The idea of EDWAM was first communicated
to one of us (CM) by Professor Lou Massa in the form of a private communication
[30].
66
C.F. Matta et al.