Excited states theory for optimized orbitals and valence optimized orbitals coupled-cluster doubles models

Abstract

We introduce an excited state theory for the optimized orbital coupled cluster doubles ͑OO-CCD͒ and valence optimized orbital coupled cluster doubles ͑VOO-CCD͒ models. The equations for transition energies are derived using a similarity transformed Hamiltonian. The effects of orbital relaxation are discussed. We present results for several single-reference molecules (H 2 O, CH 2 O, C 2 H 4 O, C 2 H 4 , BeO͒, as well as for molecules with significant nondynamical correlation in the ground state (CH ϩ , BH, Ã 1 A 1 CH 2), and for rectangular O 4 ϩ. We find that: ͑i͒ OO-CCD excitation energies are very close to CCSD excitation energies; ͑ii͒ similarly to the complete active space SCF ͑CASSCF͒ model, the effects of orbital relaxation are very important for VOO-CCD excited states such that the excitation energies calculated by VOO-CCD and CASSCF with orbitals optimized for the ground state are very close to each other and unsatisfactory; ͑iii͒ the VOO-CCD model with an approximate treatment of orbital relaxation describes singly ͑valence and Rydberg͒ and doubly ͑valence͒ excited states within errors of 0.2-1.0 eV at equilibrium geometries and along bond-breaking coordinates; ͑iv͒ the above accuracy of the VOO-CCD model does not degrade as molecules or basis sets grow in size; ͑v͒ the shapes of potential energy surfaces around excited states minima are reproduced well by VOO-CCD model suggesting the use of this method for excited states geometry optimization.

State-specific Multi-reference Perturbation Theories with Relaxed Coefficients: Molecular Applications

“…Results from the parent SS-MRCC theory are also displayed to indicate the extent of correlation captured by its perturbative counterparts. We have also shown the results of the MCQDPT2 theory of Nakano [27] using the same CAS, and VOO-CCD values of Krylov et al for both the ground as well as the 1 ∆ state [39]. From the figures one could easily discern that our SS-MRPT theories, both RS and BW, using both MP and the EN perform very well.…”

“…The performance of our SS-MRPT using these partitionings have been assessed and compared with the corresponding results of the SS-MRCC theory, in the singlesdoubles truncation scheme, and also the FCI values using the same basis, given in the paper of Krylov et al [39] as the benchmark. The basis set comprises of the standard Dunning DZP basis functions [40] 2 y as our reference functions.…”

“…The 1 ∆ state was also studied by Krylov et al [39] using the linear response version of the VOO-CCD. The excited states dominated by double excitations are not described well in any linear response theory because of [39] shows the deterioration of the quality at large C-H distance. We do not use linear response theories for this state here, and our SSMR theories remain very good throughout the PES.…”

“…For assessing the performance, the corresponding FCI results [39] with the same basis [40] have also been shown. Results from the parent SS-MRCC theory are also displayed to indicate the extent of correlation captured by its perturbative counterparts.…”

To Multireference or not to Multireference: That is the Question?

“…This is an existence proof that there is a SRCC curve that provides the right curve for SRCC. This basic idea has paid dividends in orbital optimized (OO-CC) applications [12,13], for example. (I recognize that 'variational' CC is almost an oxymoron (although XCC [3,14] and UCC [3,15] have some of those aspects) but at least at the full CI level we can see some of the consequences [16].)…”