H\"uckel--Hubbard-Ohno modeling of π\boldsymbol{\pi}-bonds in ethene and ethyne with application to trans-polyacetylene

Quantum chemistry calculations provide the potential energy between two carbon atoms in ethane (H$_3$C$-$CH$_3$), ethene (H$_2$C$=$CH$_2$), and ethyne (HC$\equiv$CH) as a function of the atomic distance. Based on the energy function for the $\sigma$-bond in ethane, $V_{\sigma}(r)$, we use the H\"uckel model with Hubbard--Ohno interaction for the $\pi$~electrons to describe the energies $V_{\sigma\pi}(r)$ and $V_{\sigma\pi\pi}(r)$ for the $\sigma\pi$ double bond in ethene and the $\sigma\pi\pi$ triple bond in ethyne, respectively. The fit of the force functions shows that the Peierls coupling can be estimated with some precision whereas the Hubbard-Ohno parameters are insignificant at the distances under consideration. We apply the H\"uckel-Hubbard-Ohno model to describe the bond lengths and the energies of elementary electronic excitations of trans-polyacetylene, (CH)$_n$, and adjust the $\sigma$-bond potential for conjugated polymers.Comment: 10 pages, 7 figures, 3 table

Variational quantum eigensolver boosted by adiabatic connection

In this work we integrate the variational quantum eigensolver (VQE) with the adiabatic connection (AC) method for efficient simulations of chemical problems on near-term quantum computers. Orbital optimized VQE methods are employed to capture the strong correlation within an active space and classical AC corrections recover the dynamical correlation effects comprising electrons outside of the active space. On two challenging strongly correlated problems, namely the dissociation of N$_2$ and the electronic structure of the tetramethyleneethane biradical, we show that the combined VQE-AC approach enhances the performance of VQE dramatically. Moreover, since the AC corrections do not bring any additional requirements on quantum resources or measurements, they can literally boost the VQE algorithms. Our work paves the way towards quantum simulations of real-life problems on near-term quantum computers

Toward more accurate adiabatic connection approach for multireference wave functions

A multiconfigurational adiabatic connection (AC) formalism is an attractive approach to computing dynamic correlation within CASSCF and DMRG models. Practical realizations of AC have been based on two approximations: i) fixing one- and two-electron reduced density matrices (1- and 2-RDMs) at the zero-coupling constant limit and ii) extended random phase approximation (ERPA). This work investigates the the effect of removing the "fixed-RDM" approximation in AC. The analysis is carried out for two electronic Hamiltonian partitionings: the group product function- and the Dyall-Hamiltonians. Exact reference AC integrands are generated from the DMRG FCI solver. Two AC models are investigated, employing either exact 1- and 2-RDMs or their second-order expansions in the coupling constant in the ERPA equations. Calculations for model molecules indicate that lifting the fixed-RDM approximation is a viable way toward improving accuracy of the existing AC approximations

The correlation theory of the chemical bond

The quantum mechanical description of the chemical bond is generally given in terms of delocalized bonding orbitals, or, alternatively, in terms of correlations of occupations of localised orbitals. However, in the latter case, multiorbital correlations were treated only in terms of two-orbital correlations, although the structure of multiorbital correlations is far richer; and, in the case of bonds established by more than two electrons, multiorbital correlations represent a more natural point of view. Here, for the first time, we introduce the true multiorbital correlation theory, consisting of a framework for handling the structure of multiorbital correlations, a toolbox of true multiorbital correlation measures, and the formulation of the multiorbital correlation clustering, together with an algorithm for obtaining that. These make it possible to characterise quantitatively, how well a bonding picture describes the chemical system. As proof of concept, we apply the theory for the investigation of the bond structures of several molecules. We show that the non-existence of well-defined multiorbital correlation clustering provides a reason for debated bonding picture