On the Vertical and Adiabatic Excitation Energies of the 2A_g State of trans-1,3-Butadiene

Abstract

The excitation energy to the 2 1 A g state of trans-1,3-butadiene is examined using a variety of ab initio electronic structure techniques. While analogous states have been shown to be the lowest singlet excited states for all longer polyenes, for butadiene the position of the 2 1 A g state relative to the HOMO f LUMO excitation (1 1 B u ) has been difficult to establish theoretically. We employ a variety of methods (CASSCF, CASPT2, MRSDCI, QDVPT) to examine both the vertical and adiabatic excitation energies for this state. At the groundstate geometry, the vertical excitation energies obtained by CASPT2 and Davidson-corrected MRSDCI for the 2 1 A g state differ by approximately 0.15 eV, but all of the methods predict that the 2 1 A g state has a lower 0-0 excitation energy than the 1 1 B u state. Possible reasons for the discrepancies between the various methods for the vertical excitation energy are discussed.

Orbital optimization in the density matrix renormalization group, with applications to polyenes and β-carotene

“…57,58 Rather, as shown by Aoyagi et al in octa-tetraene, 57 there is a lower dipole forbidden excitation, later identified as the 2A g − state, which can be rationalized in valence bond language as arising from a pair of singlettriplet excitations in the two separate double bonds that recouple to form a singlet state. [59][60][61][62][63][64][65][66][67] Following the observation of the 2A g − state in octa-tetraene, there has been much debate over the correct ordering of the 2A g − and 1B u + excited states in the shorter polyenes, compounded both by experimental difficulties in observing the dipole-forbidden 2A g − state as well as theoretical challenges in achieving a balanced description of the two states, which are dominated by very different kinds of correlation, namely, static correlation in the 2A g − state and dynamic correlation in the 1B u + state. In longer polyenes and the biologically active carotenoid and retinal pigments, questions about the low-lying spectrum are not restricted simply to the 2A g − and 1B u + state ordering.…”

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.…”

Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group

“…As a simple example, in linear polyenes, electron-electron interactions contribute to make the lowest excited singlet state ͑the 1 2A g state͒ one of double-excitation nature, rather than the singly excited highest occupied molecular orbital ͑HOMO͒ → lowest unoccupied molecular orbital ͑LUMO͒ state as one would expect in a single particle picture. [15][16][17] A more extreme example of this occurs in metallic nanotubes at low temperatures, where the qualitative electronic structure is believed to be of Luttinger liquid form. [18][19][20] Here we demonstrate that the density matrix renormalization group ͑DMRG͒, which we and others have recently been investigating in quantum chemistry, provides a solution to the question of how to flexibly and efficiently describe nondynamic correlation in systems that are large in one of their three spatial dimensions.…”