Graphene nanoribbons (GNRs), also seen as rectangular polycyclic aromatic hydrocarbons, have been intensively studied to explore their potential applicability as superior organic semiconductors with high mobility. The difficulty arises in the synthesis or isolation of GNRs with increased conjugate length, GNRs being known to have radical electrons on their zigzag edges. Here, we use a most advanced ab initio theory based on density matrix renormalization group (DMRG) theory to show the emerging process of how GNRs develop electronic states from nonradical to radical characters with increasing ribbon length. We show the mesoscopic size effect that comes into play in quantum many-body interactions of π electrons, which is responsible for the polyradical nature. An analytic form is presented to model the size dependence of the number of radicals for arbitrary-length GNRs. These results and associated insights deepen the understanding of carbon-based chemistry and offer useful information for the synthesis and design of stable and functional GNRs.

The recent advent of the density matrix renormalization group (DMRG) theory has delivered a new capability to compute multireference (MR) wave function with large configuration space, which far exceeds the limitation of conventional approaches. Here, we provide an overview of our recent work on the developments of ab initio DMRG methods in the context of the active space approaches and their applications to MR chemical systems.

A global analytic potential energy surface for the ro-vibrational dynamics of cis- and trans-formic acid is presented, constructed using LASSO-based regression to reproduce CCSD(T)(F12*)/cc-pVTZ-F12 energies. The fit is accurate to 0.25% has an RMS deviation from the ab initio data of 9 cm for the energy range 0-15000 cm. Converged J = 0 vibrational eigenstates are reported, computed using vibrational configuration interaction with an internal coordinate path Hamiltonian for the torsional motion connecting the cis and trans rotamers. Methodological choices concerning the appropriate definitions of the curvilinear and diabatic bath coordinates are discussed. The zero point of the cis rotamer is 1412 cm above that of the trans, which lies at 7354 cm. The computed fundamentals match the bands recorded from gas-phase IR spectroscopy with an RMSD of only 3 cm. A fresh assignment of the overtone spectra of both the cis and trans rotamers is presented for the energy range 0-4720 cm, where 14 out of the 51 bands are reassigned on the basis of the VCI calculations.

We propose an orbital optimized method for unitary coupled cluster theory (OO-UCC) within the variational quantum eigensolver (VQE) framework for quantum computers. OO-UCC variationally determines the coupled cluster amplitudes and also molecular orbital coefficients. Owing to its fully variational nature, first-order properties are readily available. This feature allows the optimization of molecular structures in VQE without solving any additional equations. Furthermore, the method requires smaller active space and shallower quantum circuits than UCC to achieve the same accuracy. We present numerical examples of OO-UCC using quantum simulators, which include the geometry optimization of water and ammonia molecules using analytical first derivatives of the VQE.