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First-Principles Calculations of the Energy and Width of the A Shape Resonance in p-Benzoquinone, a Gateway State for Electron Transfer Alexander A. Kunitsa, and Ksenia B. Bravaya J. Phys. Chem. Lett., Just Accepted Manuscript • Publication Date (Web): 03 Mar 2015 Downloaded from http://pubs.acs.org on March 7, 2015
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The Journal of Physical Chemistry Letters
First-Principles Calculations of the Energy and Width of the 2 Au Shape Resonance in p-Benzoquinone, a Gateway State for Electron Transfer Alexander A. Kunitsa and Ksenia B. Bravaya Department of Chemistry, Boston University, Boston, Massachusetts 02215 Abstract Quinones are versatile biological electron acceptors and mobile electron carriers in redox processes. We present the first ab initio calculations of the width of the 2 Au shape resonance in para-benzoquinone anion, the simplest member of the quinone family. This resonance state (located at 2.5 eV above the ground state of the anion) is believed to be a gateway state for electron attachment in redox processes involving quinones. We employ the equation-of-motion coupled-cluster method for electron affinity augmented by a complex-absorbing potential (CAP-EOM-EA-CCSD) to calculate resonance position and width. The calculated width, 0.013 eV, is in excellent agreement with the width of the resonant peak in the photodetachment spectrum thus supporting the assignment of the band to resonance excitation to the autodetaching 2 Au state. The methodological aspects of CAP-EOM-EA-CCSD calculations of resonances positions and widths in medium-sized molecules, such as basis set and CAP box size effects, are also discussed.
Keywords: equation-of-motion coupled-cluster, autoionization, resonances, benzoquinone, complex absorbing potential, photodetachment. Quinones are common members of electron transfer chains in biological systems
1–4
. The
most prominent examples are ubiquinones and plastoquinones. Ubiquionones serve as mobile
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intra-membrane electron shuttles transferring electrons between the protein complexes of mitochondria respiratory chain5 . Plastoquinones act as terminal electron acceptors in type II photosynthetic reaction centers3,4 . Owing to their efficiency in biological systems quinones and quinone-like compounds, e.g. catechol-containing polydopamine, have been utilized in biomimetic photosynthetic devices6,7 . Quinones’ paramount role in biological electron transfer and potential technological applications stimulated theoretical8–14 and experimental studies11,12,15–18 of electronic structure of model quinone compounds in different redox states. The simplest and the most well characterized quinone is para-benzoquinone (pBQ). Electron attachment to neutral pBQ is exothermic with adiabatic electron attachment (AEA) energy of 1.860 eV±5 meV as determined by photodetachment photoelectron studies19 of jetcooled pBQ anions. The ground state of the anion has D2h equilibrium geometry and is formed by electron attachment to the lowest π ∗ molecular orbital (MO), b2g (see Fig. 1). Excited states are generated by promoting an electron from one of the doubly occupied orbitals to the singly occupied (SOMO) π ∗ orbital (π − π ∗ or n − π ∗ excitations) or by promoting an electron from the SOMO to higher lying MOs. Previous theoretical studies8–13 consistently identify two bright states in the manifold of the low-lying excited states of the anion, 2 Au and 2
B3u , which are derived from the b2g → au and b3u → b2g one-electron excitations, respectively
(Fig. 1). Importantly, all excited states of pBQ anion (pBQ− ) are vertically unbound and lie in the electron-detachment continuum, thus, they are autodetachment resonances8–13,20 . In this Letter, we focus on the characterization of the position and width of the 2 Au resonance. Note that although the two bright states are singly excited with respect to the ground state of the anion, their decay mechanism is different. Electron detachment forming a neutral closed-shell (1 Ag ) target is a one-electron transition from 2 Au state, whereas the decay of 2 B3u is a twoelectron processes. Thus, 2 Au and 2 B3u can be classified as shape and Feshbach resonances, respectively. The latter are expected to have longer lifetimes owing to the 2-particle character of the decay which is driven by electron correlations21,22 . Despite the large positive electron affinity electron attachment to neutral pBQ proceeds more efficiently via excited electronic states of the anion. Unusual solvent, temperature, and pressure dependence of the electron attachment rates to benzoquinone 24–26 have been explained by an inverted Marcus regime for the direct electron attachment to the ground state leading to a large activation energy, and efficient electron capture via π − π ∗ excited states of the anion and their further relaxation to the ground state. Hence, the positions and lifetimes of these
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FIG. 1: Photodetachment spectrum of pBQ−19 . Vertical and adiabatic excitation energies to 2 Au and 2 B3u states, calculated at XMCQDPT2/daug-cc-pVTZ level of theory (see the text for details), are shown as solid and dotted bars, respectively. Vertical excitation energy to 2 B3u state is 2.91 eV. Adiabatic excitation energies include zero point energy (ZPE) correction computed with CASSCF(17/12)/6-311++G(2d,p) harmonic frequencies calculated for the geometries optimized at the same level of theory (see SI, Fig. S1).
metastable states are of primary importance for understanding the electron-transfer processes in quinones. Electron-detachment resonances were accurately characterized by photodetachment and resonant photodetachment photoelectron spectroscopy of the jet-cooled pBQ anions19 . pBQ− photodetachment spectrum that represents the dependence of the total yield of the ejected electrons on the excitation energy is shown in Fig. 1. The intensity in the photodetachment spectrum corresponds to the collective yield of photoelectrons with all possible kinetic energy values. The intensity, in general, rises monotonously with photon energy above the lowest detachment energy threshold in the case of direct detachment into the continuum19,27,28 . Non-monotonous features are associated with strong resonant absorption into metastable excited states of the anion followed by autoionization. Indeed, multiple sharp resonances and a single broad peak have been observed in the photodetachment spectra of pBQ− in the 2.0 - 3.0 eV region. Based on the order-of-magnitude difference in the resonances’ widths and estimated excitation energies the sharp features were assigned to Feshbach resonances, whereas the broad band at 2.5 eV was attributed to the 2 Au shape resonance. The lifetime of the state estimated from the width of the peak is 25 fs. Recent computational studies of electronic structure of pBQ and
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pBQ− also support this assignment based on the estimates of the vertical excitation energies of the anion11,12 . Yet, our multiconfigurational quasidegenerate perturbation theory calculations indicate that there are two bright states (2 Au and 2 B3u ) that absorb in this energy range. Although vertical excitation energies differ significantly, the adiabatic excitation energies are very close: 2.33 and 2.39 eV for 2 Au and 2 B3u states, respectively (Fig. 1). The simulated shapes of the 2 Au ← 2 B2g and 2 B3u ← 2 B2g transitions overlap significantly (Fig. S2). Recent time-resolved photoelectron spectroscopy studies of pBQ− demonstrated ultrafast decay of the metastable excited states on sub-40 fs timescale to the bound ground state, however, no direct estimate of shape resonance lifetime could be inferred from the experiment11 . Hence, robust theoretical prediction of the resonance position and lifetime is essential for understanding the complex picture of competing autodetachment and internal conversion in this system. This is the first attempt to characterize the widths of resonances in the pBQ− photodetachment spectrum from the first principles. We report the complex-absorbing potential equation-of-motion coupled-cluster (CAP-EOMEA-CCSD) calculations of the 2 Au resonance position and width. The CAP technique29–32 belongs to the group of methods that transform the Hamiltonian into a non-Hermitian one such that a resonance emerges as a single state with a square-integrable wave-function and complex eigenvalue: E = ER − iΓ/2
(1)
Real and imaginary parts of the complex eigenvalue are associated with resonance position (ER ) and width (Γ), respectively. Specifically, an imaginary potential absorbing the outgoing tail of the resonance wave function is added to the Hamiltonian: Hη = H − iηW
(2)
where W is chosen to have quadratic form with the size of the box defined by RX , RY , and RZ parameters: W = Wx + Wy + Wz
Wi =
0, |ri | ≤ Ri
i = X, Y, Z
(3)
(|ri | − Ri )2 , |ri | ≥ Ri
The CAP-EOM-EA-CCSD approach combines CAP technique with EOM-EA-CCSD formalism33–36 , and, thus, extends the capabilities of the method originally developed for bound
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electronic states to the description of scattering resonances. Diagonalization of the similaritytransformed CAP-modified Hamiltonian, H¯η = e−Tη Hη eTη , in the basis of 1-particle and 1-hole2-particle configurations derived from the closed-shell CAP-HF reference, yields complex electron attachment energies. Real and imaginary parts of the eigenvalue give resonance position and width, respectively (Eq. 1). Tη are coupled-cluster substitution operators with the corresponding amplitudes obtained by solving CCSD equations for the CAP-modified Hη (Eq. 2). CAP-EOM-EA-CCSD has been shown to provide accurate estimates of resonance positions and lifetimes for a test set of small molecular systems37,38 . The focus of this work is on the assignment of the resonance feature at 2.5 eV in the photodetachment spectrum of the gas-phase pBQ− . Since the results of CAP-based calculations depend on several user-defined parameters, e.g. CAP box size and a criterion used to extract resonance position and width from the η-trajectories (see below), we first discuss the performance of the CAP-EOM-EA-CCSD method and potential pitfalls in the interpretation of calculations. Specifically, we address the following: (i) criteria for distinguishing resonance and pseudocontinuum states (that can appear as false resonances) based on the results of CAPEOM-EA-CCSD calculations; (ii) the effects of the box size (CAP onset) and one-electron basis set in the quantitative prediction of resonance position and width. The calculations were performed at the optimized ground state geometry of the pBQ radical anion, unless stated otherwise. Two complementary computational approaches have been employed. Multistate multireference perturbation theory has been used for accurate characterization of the energies of the ground and the two bright excited states of the anion. The 2
B3u state leading configuration corresponds to two-electron excitation from the closed-shell
1
Ag reference: electron attachment to b2g orbital and electron promotion from b3u to b2g or-
bital (Fig. 1). This type of states is problematic for EOM-EA-CCSD method. Multireference perturbation theory approaches, on the contrary, do not suffer from this shortcoming as all possible levels of excitations within active space are treated at the same footing. The methods, however, do not account for the metastable character of the state. Thus, CAP-EOM-EA-CCSD approach has been employed to characterize the position and the width of the 2 Au resonance. 2
Au dominant configuration corresponds to a single electron attachment to the au orbital,
and, thus, the state can be reliably described with EOM-EA-CCSD and CAP-EOM-EA-CCSD methods. Specifically, the equilibrium structure was obtained using extended multireference quasidenerate perturbation theory, XMCQDPT239 , with daug-cc-pVTZ basis set. The model
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