DIP-STEOM-CCSD

TABLE 5. MR-BWCCSD and DIP-STEOM CCSD vertical transition energies (in eV) computed at the experimental equilibrium distance, and harmonic 0-0 transition energies (in parenthesis). The correlation consistent (cc-pVTZ) basis set is employed in all calculations. 

The symmetry-correct anion orbitals can also be utilized in calculations of states of the N03 cation. The primary purpose of this work is to examine the NO3 ionization spectrum and the ground and low excited states of the N03 cation system by the DIP-STEOM-CCSD method (40) (double ionization potential similarity transformed equation-of-motion coupled-cluster singles and doubles). The DIP-STEOM-CCSD method is built upon the IP-EOM-CCSD method (32) (ionization potential equation-of-motion coupled-cluster singles and doubles), which in turn, has been shown to be equivalent (41,42) to singly ionized FSMRCC, such as the example of Kaldor above. The DIP-STEOM-CCSD method generates ground and excited states of the cation by deletion of... 

In the DIP-STEOM and DIP-EOM calculations, we consider the five lowest singlet and five lowest triplet states of the cation. Cation states that are forbidden by ionization from the neutral NO3 ground state with a single photon are written as italics. To be allowed, a state must have a component involving the deletion of an electron from the anion la2 HOMO, as this is the main component of the neutral system. Table III lists the major components of the lowest DIP-STEOM-CCSD states of the cation, written as double deletions relative to the anion determinant. 

We first observe that, for both the DIP-STEOM-CCSD and DIP-EOM-CCSD results, the relative ionization potentials are very consistent between the... 

The relative IPs are also found to agree very well between the DIP-STEOM-CCSD md DIP-EOM-CCSD methods. The largest deviation is found for the two high-lying states of E symmetry. The lower of the two E states shows appreciable dependence on the basis set and differs by 0.4 eV between the DIP-SITEOM and DIP-EOM results. It is likely that the close proximity of two states of the same symmetry causes this higher sensitivity. Nevertheless, for nearly all of the states, the agreement is excellent. 

Table III. Character of the lowest DIP-STEOM-CCSD NO3 states...

In order to begin to better understand the vibrational features in the experimental PE spectrum, we now consider the DIP-STEOM-CCSD optimized geometries for the cation states. 

NOs Ground State, Dsh w DIP-STEOM-CCSD DZP T72P DIP-EOM-CCSD DZP TZ2P ... 

Table V. DIP-STEOM-CCSD/TZ2P optimized geometries and adiabatic electronic IPs for the state...

As seen previously, the vertical DIP-STEOM-CCSD calculations find the E" state to be very close in energy to the E" state (see Table II). This result is supported by the DIP-EOM-CCSD calculations as well. We again note the discrepancy with the DFT calculations of Wang (5) and the MCSTEP results of Heryadi (7). These other results may be questioned, however, as previously discussed. We are left with the suggestion that the E" state contributes to the lower-energy peaks in the region of 13.18 eV observed in the PE spectrum (see Figure 2). 

Table VI. DIP-STEOM-CCSD/TZ2P vibrational frequencies (cm" ) at the minimum ( 2) and transition state ( 2) stationary points, Jahn-Teller split from the D311 conical intersection...

The DIP-STEOM-CCSD/TZ2P optimized geometries of all components of the three states are collected in Table VII. Vibrational frequency calculations verify the A2 state to be a true minimum in symmetry. The doubly degenerate E" and E electronic states, on the other hand, will undergo Jahn-Teller distortion in the non-symmetric e vibrational coordinates. The Dsh... 

In contrast to the E" 1L2S minimum in DIP-STEOM-CCSD, a recent DFT study (14) reported a significantly distorted 1S2L structure for the E" state (Ri=1.152 A R2=R3=1.315 A Ai2=Ai3=132°). It is unclear if the stationary point was verified to be a true minimum by vibrational frequency calculations. As an additional confirmation of the DIP-STEOM-CCSD results, we also performed DIP-EOM-CCSD geometry optimizations and vibrational frequency calculations on the E" state. The DIP-EOM method finds C2v minimum and transition state structures nearly identical to the DIP-STEOM results in Table VII. 

Table VIII. DIP-STEOM-CCSD/TZ2P conical intersections of the...

The NO3 vertical ionization spectrum was calculated by the DIP-STEOM-CCSD and DIP-EOM-CCSD methods. These methods avoid artifactual symmetry breaking of the reference wavefunction by starting from the symmetry-correct nitrate anion orbitals and provide a balanced treatment of dynamical and non-dynamical correlation effects. In general, the DIP-STEOM and DIP-EOM results agree well with the experiment of Wang (5) and with previous theoretical assignments (5,7). However, in our calculations, the vertical transition to the E" state nearly coincides with that of the E" state, in contrast to previous studies. Our calculations therefore do not support the assignment of the broad experimental feature near 14.05 eV to the E" state. 

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