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The molecules 1,4-cyclohexadiene (unconjugated 1,4-CHD) and 1,3-cyclohexadiene (conjugated 1,3-CHD) both have two double bonds, but these bonds interact in different ways. These molecules have long served as examples of through-bond and through-space interactions, respectively, and their electronic structures have been studied in detail both experimentally and theoretically, with the experimental assignments being especially complete. The existence of Rydberg states interspersed with the valence states makes the quantum mechanical calculation of their spectra a challenging task. In this work, we explore the electronic excitation energies of 1,4-CHD and 1,3-CHD for both valence and Rydberg states by means of complete active space second-order perturbation theory (CASPT2), extended multi-state CASPT2 (XMS-CASPT2), and multiconfiguration pair-density functional theory (MC-PDFT); it is shown by comparison to experiment that MC-PDFT yields the most accurate results. We found that the inclusion of Rydberg orbitals in the active space not only enables the calculation of Rydberg excitation energies but also improves the accuracy of the valence ones. A special characteristic of the present analysis is the calculation of the second moments of the excited-state orbitals. Because we find that the CASPT2 densities agree well with the CASSCF ones and since the MC-PDFT methods gets accurate excitation energies based on the CASSCF densities, we believe that we can trust these moments as far as giving a more accurate picture of the diffuseness of the excited-state orbitals in these prototype molecules than has previously been available.
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Generalization of the tensor product selected CI method for molecular excited states
In a recent paper (JCTC, 16, 6098 (2020)), we introduced a new approach for accurately approximating full CI ground states in large electronic active-spaces, called Tensor Product Selected CI (TPSCI). In TPSCI, a large orbital active space is first partitioned into disjoint sets (clusters) for which the exact local many-body eigenstates are obtained. Tensor products of these locally correlated many-body states are taken as the basis for the full, global Hilbert space. By folding correlation into the basis states themselves, the low-energy eigenstates become increasingly sparse, creating a more compact selected CI expansion. While we demonstrated that this approach can improve accuracy for a variety of systems, there is even greater potential for applications to excited states, particularly those which have some excitonic character. In this paper, we report on the accuracy of TPSCI for excited states, including a far more efficient implementation in the Julia programming language. In traditional SCI methods that use a Slater determinant basis, accurate excitation energies are obtained only after a linear extrapolation and at a large computational cost. We find that TPSCI with perturbative corrections provides accurate excitation energies for several excited states of various polycyclic aromatic hydrocarbons (PAH) with respect to the extrapolated result (i.e. near exact result). Further, we use TPSCI to report highly accurate estimates of the lowest 31 eigenstates for a tetracene tetramer system with an active space of 40 electrons in 40 orbitals, giving direct access to the initial bright states and the resulting 18 biexcitonic states.
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- Award ID(s):
- 1752612
- PAR ID:
- 10406649
- Date Published:
- Journal Name:
- arXivorg
- ISSN:
- 2331-8422
- Page Range / eLocation ID:
- arXiv:2303.02232
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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