Coupled-cluster calculations of the excitation energies of ethylene, butadiene, and cyclopentadiene

Abstract

The equation-of-motion coupled-cluster ͑EOM-CC͒ method has been used to calculate the vertical excitation energies of ethylene, trans-butadiene, cis-butadiene, and cyclopentadiene. The approximations used were the EOM-CC singles-and-doubles ͑EOM-CCSD͒ method and EOM-CCSD with a noniterative treatment of triple excitations, EOM-CCSD͑T͒, EOM-CCSD͑T͒. The basis sets were atomic natural orbital sets augmented with diffuse functions. Comparisons have been made with a series of complete active space second-order perturbation theory ͑CASPT2͒ results, which used the same basis sets and geometries, and experiment. For the Rydberg states the EOM-CCSD results were in good agreement with experiment and CASPT2. The results for the valence states show more variation. For ethylene CASPT2 exaggerates the Rydberg character of the V state, while EOM-CCSD provides a better description. For the valence states of the other molecules the EOM-CCSD excitation energies tend to be too high, but considerable improvements are given by EOM-CCSD͑T͒. For the 1 1 B u /1 1 B 2 states of butadiene and cyclopentadiene EOM-CCSD͑T͒ agrees well with experiment and CASPT2. The agreement for the 1 1 A g →2 1 A g and 1 1 A 1 →2 1 A 1 transitions for trans-butadiene and cis-butadiene, which are not known experimentally, is not so good, with the EOM-CC results significantly higher than the CASPT2 ones. However, the EOM-CCSD͑T͒ and CASPT2 energies for the 1 1 A 1 →2 1 A 1 transition in cyclopentadiene are in quite close agreement and both agree well with experiment. EOM-CCSD͑T͒ shows an average error in vertical excitation energies for all states of all molecules of 0.12 eV, and improves those for valence states from an error of 0.26 eV for EOM-CCSD to 0.13 eV.

Excited States of Butadiene to Chemical Accuracy: Reconciling Theory and Experiment

“…Our main results are presented using the same experimental geometry as is used widely in previous theoretical studies, 1,2 and derived from the 1966 experimental data of Haugen and Traetteberg. 3 We made this choice to facilitate easier comparison with previous studies, but the choice of geometry could potentially affect the results on a scale of 0.1 eV, so we explored two other theoretically optimized geometries in addition.…”

On the difference between the transition properties calculated with linear response- and equation of motion-CCSD approaches

“…For the first four systems ͑up to five double bonds͒, the experimental transition energies in gas phase are known. [11][12][13][14][15][16][17][18][19] Table IV reports the experimental as well as the calculated vertical transition energies. Figure 3 shows the shift in the transition energies with respect to butadiene.…”

Double excitations within time-dependent density functional theory linear response

“…The low-lying electronic states of many conjugated molecules exhibit significant double excitation character in wave function treatments. 23,24,[27][28][29][30] A classic example is the family of polya͒ Electronic mail: nmaitra@hunter.cuny.edu enes. The lowest-lying singlet state of all polyenes is not a simple one-electron excitation from the highest occupied to the lowest unoccupied orbital of the ground state, but has a large zeroth-order contribution from a doubly excited determinant.…”