13586 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA J. Phys. Chem. zyxwvut 1993, 97, 13586-13597 Butadiene. 3. Charge Distribution in Electronically Excited States Kenneth B. Wiberg,' Christopher M. Hadad,$ G. Barney Ellison,$ and James B. Foresman Department of Chemistry, Yale University, New Haven, Connecticut 0651 1 Received: September 30, 1993' zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA The vertical transition energies for butadiene have been calculated using the CIS/6-3 1 1 (2+)G* theoretical model. The observed energies were satisfactorily reproduced. The charge distribution for each of the excited states was calculated so that the change from the ground-state distribution could be examined. The nature of the Rydberg states are discussed. Quantitative information on the degree of charge-transfer and bond-order changes was obtained for the excited states. The adiabatic geometries of the valence and Rydberg states were examined, and vibrational frequencies for the excited states were calculated, providing agreement with experiment. The triplet states were also studied for both the vertical and adiabatic surfaces. Analysis of the charge density gave information on the charge reorganization that occurs in the excited states. It showed the remarkable similarity of the atomic orbital-like Rydberg states to the corresponding radical cation and, moreover, showed the unique nature of the 1'B, A zyxwvutsrq - A* valence state. The vertical 2lA, state was examined with the MCSCF method. For a comparison, the 1 'B", 13B,, and 13A, states were studied in the same fashion. The relationship between these states is discussed. Introduction As the simplest of the chemically important polyenes, the electronicallyexcited states of butadiene have received extensive experimental' and theoretical study.* The ground state of butadiene has A, symmetry, and the electronicallyexcited states may have A,, A,, B,, or B, symmetry. For a one-photon process the transition moment is zero for a g - g* transition, and only transitions to an A, or B, states are allowed. The B, states are in-plane zyxwvutsrqp (x,y) polarized and the A,, states are out-of-plane (2) polarized. The B, states are expected to be relatively intense since the transition dipole length can approach half the length of the *-system. The A, transitions are expected to be relatively weak since the transition moment length in the z direction must of necessity be small. The electronic spectrum of butadiene is shown in Figure 1. It is now generally agreed that the first allowed excited state corresponds to the B, A - A* transition. The zyxwvut 0,O transition is at 46 258 cm-1 (5.74 eV) and the vertical transition is at 47 678 cm-1 (5.91 eV). This is followed by some weaker bands and then by a set of A, Rydberg transitions starting at 56 970 cm-l (7.06 eV Table I). In the simple *-electron approximation, the A* excited state is formed by taking an electron from an MO which has a node between C2 and C3 and placing it in an MO which has nodes between C1 and C2 and between C3 and Cd. Thus, one would expect increased double-bond character between C2 and C3 and decreased double-bond character between the other C-C bonds. We were interested in seeing how large a charge shift actually occurs. Rydberg states are important in the electronic spectrum of butadiene and of other h y d r ~ a r b o n s . ~ In the case of atoms Rydberg states are formed by transitions from occupied atomic orbitals to virtual atomic orbitals, and with approximately spherical molecules, one could visualizetransitions from occupied orbitals to diffuse atomic-orbital-like configurations. However, with an extended planar systems such as butadiene, it is not as clear as to what is meant by a Rydberg state. Here again, a study of the charge distribution in the excited states should be. useful. The geometries of the excited states of butadiene have been extensively disc~ssed.~ While octatetraene and longer polyenes fluoresce, butadiene does not. The lack of fluorescence of the A - A* state has been attributed to nonradiative energy transfer f Department of Chemistry, University of Colorado, Boulder, CO 80309. @ Abstract published in Advance ACS Abstracfs, December I, 1993. 0022-365419312097-13586$04.00/0 80.0 . 70.0. - 60.0. 5 50.0. 40.0. zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJI z 6 0 30.0. VI FREQUENCY [CM-1 X 10-31 Figure 1. Electronic spectrum of 1,3-butadiene along with a comparison of theexperimentalandcalculated (CIS/6-311(2+)G*) vertical transition energies for the singlet excited states. The average error of the CIS energies (0.2 eV) corresponds to 1600 cm-I. to a different excited state which is of a similar geometry.1° The low-energy region of the absorption spectrum is quite broad for butadiene, and the bandwidth becomes significantly narrower for hexatriene and octatetraene.Ij The bandwidth of butadiene also is relatively unaffected by temperature. The cause of the large bandwidth is not known. Also, while some vibrational frequencies for the A - A* state are known, thedegreeof twisting of the carbon framework has been debated.1j~0~2j,k.q The recent implementation of the configuration interaction with singles (CIS) excitation method,5and its success in thestudy of the excited states of bicyclo[ 1.1 .O]b~tane,~ ethylene,' form- aldehyde, acetaldehyde,8 and pyridine5 has prompted our study of butadiene. We have now examined its vertical and adiabatic excited states. Other procedures such as MRD-C12m have the potential of giving somewhat more accurate transition energies. However, our main interestis in learning more about the properties of excited states, and the CIS formalism is particularly well suited for studiesof adiabatic geometries and of excited-statevibrational frequencies. Calculated Transition Energies and Intensities The effect of basis set on the calculated transition energies was examined, and as with the other molecules we have studied, it was necessary to include a double set of diffuse functions in order zyxwvutsrqpo 0 1993 American Chemical Society