Description Of Rydberg States Research Articles

Accuracy of Coupled Cluster Excitation Energies in Diffuse Basis Sets.

We present a comprehensive statistical analysis on the accuracy of various excited state Coupled Cluster methods, accentuating the effect of diffuse basis sets on vertical excitation energies of valence and Rydberg-type states. Many popular approximate doubles and triples methods are benchmarked with basis sets up to aug-cc-pVTZ, with high level EOM-CCSDT results used as reference. The results reveal a serious deficiency of CC2 linear response and CIS(D) techniques in the description of Rydberg states, a feature not shown by the EOM-CCSD(2) and EOM-CCSD variants. The CC3 theory proves to be an accurate choice among the iterative approximate triples methods, while the novel perturbation-based CCSD(T)(a)* variant turns out to be the best way to include the effect of triple excitations in a noniterative way.

Investigation of the Impact of Different Terms in the Second Order Hamiltonian on Excitation Energies of Valence and Rydberg States.

Describing electronically excited states of molecules accurately poses a challenging problem for theoretical methods. Popular second order techniques like Linear Response CC2 (CC2-LR), Partitioned Equation-of-Motion MBPT(2) (P-EOM-MBPT(2)), or Equation-of-Motion CCSD(2) (EOM-CCSD(2)) often produce results that are controversial and are ill-balanced with their accuracy on valence and Rydberg type states. In this study, we connect the theory of these methods and, to investigate the origin of their different behavior, establish a series of intermediate variants. The accuracy of these on excitation energies of singlet valence and Rydberg electronic states is benchmarked on a large sample against high-accuracy Linear Response CC3 references. The results reveal the role of individual terms of the second order similarity transformed Hamiltonian, and the reason for the bad performance of CC2-LR in the description of Rydberg states. We also clarify the importance of the T̂1 transformation employed in the CC2 procedure, which is found to be very small for vertical excitation energies.

Theoretical investigation of the electronic spectrum of pyrazine

The description of Rydberg states by the complete active space self-consistent field (CASSCF) electronic structure method is known to be a difficult topic. In particular, two problems are frequently encountered: (a) the simultaneous presence of valence and Rydberg excited states in the same energy region can potentially lead to artificial valence–Rydberg mixing in the electronic wave functions. (b) Rydberg states have a tendency to be difficult to converge. We have implemented an approach for the consistent description of both valence and Rydberg excited states within the CASSCF electronic structure model. By employing the multiconfigurational second- and third-order perturbation theory (CASPT2/3) methods based on CASSCF reference wave functions, the procedure is verified by comparison with spectroscopic results for the example molecule pyrazine. Vertical excitation energies and other properties have been calculated for various electronic states. Basis sets and active spaces were selected to provide accurate results. Two combinations of aug-cc-pVTZ level basis sets complemented by Rydberg functions have been employed to calculate estimates for the properties of 19 singlet excited states of pyrazine. While many of the assignments made in previous studies could be confirmed, there are also several new aspects emerging from the present investigation.

Pseudopotential Theory of Atomic and Molecular Rydberg States

In this paper we present a description of atomic and molecular Rydberg states using an effective Hamiltonian in the one-electron Hartree—Fock approximation. A pseudopotential is introduced to ensure the orthogonality of the Rydberg orbitals to the core. The core is represented by the ground-state wavefunction of the corresponding positive ion. In order to incorporate the pseudopotential formalism in a description of Rydberg states, the original pseudopotential theory is extended to the case where the core and valence orbitals are eigenfunctions of different one-electron operators. The formalism is applied to the triplet S states of helium and beryllium atoms and the results of numerical calculations are given. Good agreement with experiment is found. Possible extensions of the theory to more complex systems are discussed.