The effects of higher orders of perturbation theory on the correlation energy of atoms and bonds in molecules

• Published in: International journal of quantum chemistry 2018-04, Vol.118 (8), p.n/a
• Main Authors: Vincent, Mark A., Silva, Arnaldo F., McDonagh, James L., Popelier, Paul L. A.
• Format: Article
• Language: English
• Subjects: Chemical bonds; Chemistry; Convergence; Correlation; Digital music; Energy; glycine; interacting quantum atoms; MP3; MPn; Perturbation theory; Physical chemistry; QTAIM; quantum chemical topology; Quantum physics
• ISSN: 0020-7608; 1097-461X
• DOI: 10.1002/qua.25519

We examine, for the first time, the effects of higher orders of Møller–Plesset perturbation theory on the individual atoms within a molecule and the bonds between them, via the topological energy partitioning method of interacting quantum atoms. In real terms (i.e., not by absolute value) MP3 decreases the correlation energy of a bond, and MP4SDQ also decreases the energy of the atoms at either end of the bond. In addition, we investigated long‐range through‐space dispersive effects on a H2 oligomer. Overall, MP3 is the largest correction to the correlation energy, and most of that energy is allocated to chemical bonds, reducing their values in actual terms. The MP4SDQ bond correlation correction, despite being relatively small, tends to have two effects: (i) for small or negative correlation energies MP4SDQ tends to decrease the bond correlation values even more, and (ii) for large (positive) bond correlation energies MP4SDQ tends to restore the bond correlation energies from the MP3 back toward the MP2 values. Furthermore, each individual part of a molecule or complex (atom or bond) has a specific convergence pattern for the MPn series: through‐space interactions converge at MP2 but bonds converge at MP3 level. The atomic correlation energy appears to head toward convergence at the MP4 level. The two‐particle density matrix is extracted from GAUSSIAN and used to topologically partition (interacting quantum atoms) the electron correlation of MP2, MP3, and MP4 wave functions of small molecules and glycine. Great technical care is taken. The results shed novel light on how MP2, MP3, and MP4 wave functions describe both atoms and bonds.