Comparison of CIS- and EOM-CCSD-Calculated Adiabatic Excited-State Structures. Changes in Charge Density on Going to Adiabatic Excited States Kenneth B. Wiberg,* ,² Yi-gui Wang, ² Anselmo E. de Oliveira, ²,‡ S. Ajith Perera, § and Patrick H. Vaccaro* ,² Department of Chemistry, Yale UniVersity, New HaVen, Connecticut 06520-8107, and The Quantum Theory Project, UniVersity of Florida, GainsVille, Florida 32611 ReceiVed: August 17, 2004 The CIS and EOM-CCSD adiabatic geometries for the first excited states of a set of small molecules (C 2 H 4 , C 2 H 2 ,H 2 CdO, H 2 CdS, CS 2 , CO 2 , SO 2 , NO 2 ) have been calculated using the 6-311++G** basis set to see if the former geometries can be good starting points for optimizations at the latter theoretical level. With most of the molecules, there is fairly good agreement between the results from the two methods, and EOM- CCSD gives good agreement with the available experimental data. A detailed discussion of the lowest-lying singlet excited states in CO 2 and CS 2 is presented, highlighting the pronounced differences in electronic character and equilibrium structure displayed by these isovalent species. The origins of the structural distortions that are frequently found for the adiabatic excited states are examined with the aid of deformation density plots and the electron localization function (ELF). 1. Introduction Electronically excited states frequently have significantly different structures than ground states. For example, the π* r n state of formaldehyde is known to have a pyramidal structure, 1 and the π* r π state of acetylene has a bent structure. 2 CIS 3 and EOM-CCSD 4 represent two extremes in single-reference models for calculating the structures and energies of electroni- cally excited states. CIS is computationally inexpensive and allows facile geometry optimizations for excited states in addition to giving vibrational frequencies. However, it often leads to significant errors in the calculated transition energies. 5 EOM-CCSD is very effective in reproducing experimental transition energies, 6 but it is also computationally intensive, making it relatively difficult to use to obtain the structures of excited states. We have examined the question of whether the CIS-optimized structures for the adiabatic excited states would provide good starting points for EOM-CCSD geometry optimizations for these states. The calculations were carried out using the 6-311++G** basis set, which has been found to give good transition energies for CCSD-EOM calculations of valence states and the lower- energy Rydberg states. 7 It might be noted that this basis set gives lower total energies and generally more satisfactory ground-state geometries than aug-cc-pVDZ, 8 and it also gives lower energies for excited states. The higher-energy Rydberg states require the addition of more diffuse functions to obtain satisfactory calculated transition energies. 7 However, these states are not of concern in this report. 2. Ethylene Ethylene is one of the most studied of organic compounds. The equilibrium CdC bond length has been derived from experimental data, 9 and many calculations have been reported. 10 The electronically excited states have received extensive study, both experimentally 11 and theoretically. 11 The lowest-energy transition is to a 3s r π Rydberg state, and this is followed by the π* r π excited state. The latter is known to be twisted 12 to minimize the interaction between the singly occupied π and π* orbitals. The former has also been found to be twisted, but to a smaller degree than the π* r π excited state. Experimental information concerning the geom- etries of these excited states is available, 12 and they are com- pared with the results of CIS and EOM-CCSD calculations in Table 1. The HF level for the ground state corresponds to the CIS level for the excited states. The HF carbon-carbon double bond is short as is normally found for multiple bonds at this level of theory. 13 The CCSD-calculated length is in very good agreement with the observed value. The adiabatic π* r π excited state is known to be twisted, and both CIS and CCSD give structures twisted by ∼90°. The CdC bond length was found to be somewhat increased in the excited state. EOM-CCSD gives a slightly enlarged bond, whereas CIS gives a considerably elongated bond. The planar transition state for rotation about the CdC bond is calculated to have an energy about 14 000 cm -1 higher than the adiabatic state and to be considerably elongated. The adiabatic 3s r π Rydberg state is known to have a Cd C bond length of 1.41 Å, and this is reproduced by both CIS and EOM-CCSD. The EOM-CCSD potential energy curve for twisting the CdC bond has a very shallow minimum at 27° (Figure S1, Supporting Information), in good agreement with the experimental results. The CIS calculation gives only a planar structure for this state. 3. Acetylene An analysis of the structure of the A ˜ 1 A u π* r π transition for acetylene has shown that it adopts a trans-bent geometry. 2 * To whom correspondence should be addressed. E-mail: kenneth.wiberg@yale.edu (K.W.). ² Yale University ‡ Present address: Instituto de Quimica-UFG, Goiania, GO, Brazil. § University of Florida. 466 J. Phys. Chem. A 2005, 109, 466-477 10.1021/jp040558j CCC: $30.25 © 2005 American Chemical Society Published on Web 12/31/2004