Background
Although a lot of interesting chemically relevant information can be extracted already from the analysis of first order density matrix (e.g. various forms of population analyses, Bader's quantum topology etc.) some more subtle structural features related to the effects of mutual coupling of electron motions are available only from the analysis of second order or pair density matrix. The most attractive feature of these matrices is that because of explicit inclusion of two electrons they are especially useful for the analysis of all the effects where the correct description of pair behavior is important. Such is, e.g., the case in the discussion of the role of electron pairing in chemical bonds and, also, in the evaluation of the role of correlation effects during structural transformations.
Relevant publications
Ponec R., Strnad M.:
Population Analysis of Pair Densities. A link
between Quantum Chemical and Classical Picture of
Chemical Structure. Int. J. Quant. Chem. 50, 43 (1994)
Ponec R.: Electron Pairing and
Chemical Bonds. Coll. Czech. Chem. Commun. 59,
505 (1994)
Ponec R., Bochicchio R.:
Nonlinear Population Analysis from Geminal
Expansion of Pair Densities. Int. J. Quant. Chem.
54, 99 (1995)
Ponec R., Jug K.:
Population Analysis of Pair Densities. A New Way
of Visualization of Molecular Structure. Int. J.
Quant. Chem. 60, 75 (1996)
Ponec R.: Electron
Reorganization in Chemical Reactions. Pair
Population Analysis along Concerted Reaction Path
of Allowed and Forbidden Pericyclic Reactions.
Int. J. Quant. Chem. 62, 171 (1997
Ponec R., Mayer I.:
Investigation of some Properties of Multicenter
Bond Indices J. Phys. Chem. A 101, 1738 (1997)
Ponec R.: Electron Pairing
and Chemical Bonds. Molecular Structure from the
Analysis of Pair Densities and Related Quantities.
J. Math. Chem. 23, 85 (1998)
Ponec R.: Electron Pairing
and Chemical Bonds. Chemical Bonds from the
Condition of Minimum Fluctuation of Electron
Pairs. Int. J. Quant. Chem. 69, 193 (1998)
R. Ponec: Electron Pairing
and Chemical Bonds. Molecular Structure from the
Analysis of Pair Densities and Related Quantities.
J. Math. Chem. 23, 85 (1998).
A. Bochicchio, R. Ponec, L.
Lain, A. Torre: On the Physical Meaning of Bond
Indices from the Population A. Bochicchio, R.
Ponec, L. Lain, A. Torre: nalysis of Higher Order
Densities. J. Phys. Chem. A 102, 7176 (1998).
R. Ponec: Electron Pairing
and Chemical Bonds. Chemical Bonds from the
Condition of Minimum Fluctuation of Electron Pair
69, 193 (1998).
Ponec R., Bochicchio R.:
Nonlinear pair population analysis. The study of
basis set dependence. (Eng) Int. J. Quant. Chem.
72, 127-137 (1999).
Ponec R., Carbó-Dorca R.:
Chemical bonds from the condition of minimal pair
fluctuation. Correlated case. (Eng) Int. J. Quant.
Chem. 72, 85-91 (1999).
Ponec R., Duben A.J.:
Electron pairing and chemical bonds.Bonding in
hypervalent molecules from the analysis of the
Fermi holes. (Eng) J. Comput. Chem. 20(8), 760-771
(1999).
Torre A., Lain L.,
Bochicchio R., Ponec R.: On the nature of
nonclassical bonds in closo-boranes: A nonlinear
population analysis approach. (Eng) J. Comput.
Chem. 20, 1085-1090 (1999)
Ponec R., Roithová J.,
Sannigrahi A.B., Lain L., Torre A., Bochicchio R.:
On the nature of multicenter bonding in simple
atomic clusters. (Eng) Theochem 505, 283-285 (2000).
Bochicchio R., Lain L.,
Torre A., Ponec R.: Picture of bonding in
protonated phosphorus and arsenic clusters.
Detection of 3-center bonds from the generalized
population analysis. (Eng) Croat. Chem. Acta 73(4),
1039-1046 (2000).
La Manna G., Di Gregorio G.,
Ponec R.: Population analysis of pair densities.
A study on cyclic systems. (Eng) J. Mol. Struct.
Theoch. 499, 233-240 (2000).
Bach A., Amat L., Carbó-Dorca
R., Ponec R.: Quantum chemistry, Sobolev spaces
and SCF. (Eng) J. Math. Chem. 28(1-3), 59-70 (2000).
Bochicchio R., Lain L.,
Torre A., Ponec R.: Topological population
analysis from higher order densities I: Hartree-Fock
level. (Eng) J. Math. Chem. 28(1-3), 83-90 (2000).
Bochicchio R., Ponec R.,
Lain L., Torre A.: Pair population analysis
within AIM theory. (Eng) J. Phys. Chem. A 104,
9130-9135 (2000).
Ponec R., Roithová J.:
Domain averaged Fermi-holes - a new means of
visualization of chemical bonds. Bonding in
hypervalent molecules. (Eng) Theor. Chem. Acc.
105, 383-392 (2001)
Ponec
R., Roithová J., Haas Y.: Mechanism of gas phase
ethene-ozone reaction and concomitant processes.
Theoretical study. (Eng) Croat. Chem. Acta. 74,
251-264 (2001)
Bochicchio R., Ponec R.,
Torre A., Lain L.: Multicenter bonding within the
AIM theory. (Eng) Theor. Chem. Acc. 105, 292-298
(2001)