Employing broken symmetry effects from unrestricted coupled cluster wave function to determine dynamic and non‐dynamic electron correlation during triple bond breaking in the N₂ molecule

Abstract

The cluster structure of the singlet full symmetric component of the unrestricted Hartree‐Fock (UHF)‐based CCSD wave function describing the triple bond breaking in the nitrogen molecule has been subjected to a detailed analysis for the possibility of determining the dynamic and near‐degeneracy electron correlation. The results obtained show that the spin and symmetry contaminations are not responsible only for the appearance of the artificial hump in the potential energy curve (PEC) generated by the UHF‐based CCSD calculations. A theoretical analysis of this issue indicates that the UHF‐based CCSD wave function and its singlet full symmetric component have a multi‐reference structure. This form of the wave function allows to explain the mechanism for creating cluster contributions in the projected UHF‐based CCSD wave function, which also provides the opportunity to explain the cause of the hump in the nitrogen PEC generated by the UCCSDecCCSD method.

Reasons Why Most Single-Reference Coupled Cluster Methods Fail to Provide the Correct Adiabatic Potentials of a Diatomic Carbon Molecule: UCCSDecCCSD Potential Study

“…Therefore, in the following considerations, we will mainly focus on these contributions. Moreover, it should be noted that the values of the additivity parameters 42 ΔE add PUCCSD and Δ add PUCCSD are very small in the geometry range to the avoided crossing point [cf. Table 2].…”

“…Therefore, by appropriately grouping the connected and disconnected excitations given in the UHF-based CCSD equations with the T 1 UHF and T 2 UHF cluster contributions, 41,42 we can transform the exponential UHF-based CCSD wave function…”

“…All the calculations concerning the diatomic carbon molecule and H8 model system were performed using the Dunning double ζ (DZ) basis function set. 54 The choice of the DZ basis set here is a demanding case due to the large dominance of the projected UHF (PUHF) contribution in the PUCCSD wave function, 42 which may also lead to situations where the T 4…”

Extraction of a One-Particle Reduced Density Matrix from a Quantum Monte Carlo Electronic Density: A New Tool for Studying Nondynamic Correlation

“…com/article/10.3390/computation9120135/s1. This file contains detailed information on: (1) The geometries of the molecules in xyz format, (2) The VMC wave function used in this work, (3) The electronic densities computed at QMC level, (4) Tables with the global indicators of correlation for CASSCF and QMC results, (5) The local indicators of correlation calculated with the QMC results, (6) The global indicators of correlation computed at UKS-DFT level as well as the mean values of the S 2 operator and the difference between the restricted and unrestricted energies, (7) The results of the fit of the Fermi distribution and the corresponding plots.…”

“…However, it is possible to evaluate the spin contamination between different spin states through the evaluation of the expectation values < Ŝ2 >. It was shown that this approach allows including correlation for some particular systems, but its results are inadequate for others (see, for example, [5][6][7]). In the case of spin contamination we speak of symmetry breaking and in KS theory we can interpret the difference between restricted and unrestricted energy as an estimate of nondynamic correlation energy, namely…”