Complex Absorbing Potential Equation-of-Motion Coupled-Cluster Method Yields Smooth and Internally Consistent Potential Energy Surfaces and Lifetimes for Molecular Resonances.

The recently developed equation-of-motion electron-attachment coupled-cluster singles and doubles (EOM-EA-CCSD) method augmented by a complex absorbing potential (CAP) is applied to the Πg resonance of N2 and the Σu resonance of H2 at various internuclear distances. The results illustrate the advantages of EOM-CC for treating resonance states over statespecific approaches. CAP-EOM-EA-CCSD produces smoothly varying potential energy curves and lifetimes for both Σ and Π resonances. The computed lifetimes and energy differences between the neutral and electron-attached states are internally consistent, that is, the resonance width becomes zero at the same internuclear distance where the energy of the electron-attached state drops below that of the neutral state. Such smooth and internally consistent behavior is only achieved when the perturbation due to the CAP is removed using the first-order deperturbative correction that we introduced earlier; the evaluation of resonance positions and widths from raw (uncorrected) energies leads to unphysical discontinuities and fails to correctly describe the conversion of a resonance to a bound state at large internuclear distances. SECTION: Spectroscopy, Photochemistry, and Excited States T anions formed by electron attachment to a neutral closed-shell molecule with negative electron affinity play an important role in multiple areas, including plasma physics, atmospheric chemistry, and biology. The resulting electronic states have finite lifetimes and are called resonances. These states belong to the continuum part of the spectrum; therefore, their wave functions are not Lintegrable. Using the Siegert (imposing outgoing wave boundary conditions) or Feshbach (a bound state diabatically coupled to the continuum) formalisms, a resonance can be described similar to a bound state but with a complex energy that gives rise to an exponential decay in time ψ = Ψ = Ψ − − Γ − r t r r ( , ) e ( ) e e ( ) Et t E t i res ( /2) i res R (1) In this formulation, the resonance position ER and width Γ are obtained from the real and imaginary parts of the energy eigenvalue of the time-independent Schrödinger equation. In order to avoid working with continuum functions or dealing with boundary conditions, a number of approaches that treat resonances using L methods have been developed. These include stabilization techniques, using small bases and artificial real stabilizing potentials, complex scaling, and complex absorbing potential (CAP) methods. Complex scaling where one scales all coordinates in the Hamiltonian by a complex number has rigorous theoretical foundation, but is plagued by an extreme basis set dependence and conceptual difficulties in describing molecular resonances and, especially, potential energy surfaces (PESs). In contrast, CAP methods do not suffer from such problems and can be easily implemented within standard quantum-chemical methods. In CAP methods, the molecular Hamiltonian H0 is augmented by an artificial imaginary potential W that absorbs the diverging tail of the resonance wave function, converting it into an L-integrable form η η = − H H W ( ) i 0 (2)