Time-Dependent Density Functional Theory Investigation of the Ground and Excited States of Coumarins 102, 152, 153, and 343

We present calculations of various properties of the ground and excited electronic states of coumarins 102, 152, 153, and 343. Using density functional theory (DFT) and time-dependent density functional theory (TDDFT), we examine the excitation energies to the S1 and S2 states, the ground and excited-state dipole moments, and the lowest ionization potentials of these coumarins. In the case of C153, we locate two distinct S0 minima due to differing conformations of the julolidyl ring structure and compare properties for the syn and anti conformers. For C343, we examine the possibility of proton transfers in the ground and S1 states of the system. We find that (1) DFT tends to overestimate the ground-state dipole moments in these systems, (2) excellent agreement is obtained between TDDFT and experimental vertical excitation energies, (3) TDDFT and CIS yield similar estimates of the dipole moment change between the S0 and S1 states, both of which are in the range of previous experimental estimates, (4) in each case, the S2 state is at least 0.5 eV above the S1 state for the ground-state geometry, and (5) proton transfer is not likely in the ground state of C343 but is only 0.18 eV higher in energy in the S1 state. We also compare the DFT/TDDFT results with RHF/CIS, MP2, and INDO S/CI results. We find good agreement between MP2 and experimental ground-state dipole moments and good agreement between INDO S/CI and TDDFT gas-phase excitation energies

Size‐Inconsistency Effects in Molecular Properties for States with Valence‐Rydberg Mixing: The Low‐Lying π→π∗ States of Ethylene and Butadiene

Ab initio results for the low‐lying 1B1u states of ethylene are used to discuss size‐inconsistency effects on calculated molecular properties for states where valence‐Rydberg mixing is important. Results for the expectation value of x2, x being the coordinate perpendicular to the plane of the molecule, are presented from quasidegenerate variational perturbation theory and multireference configuration‐interaction calculations. These results are compared with values from previous studies. It is argued that size inconsistency in configuration‐interaction studies can have a significant effect on estimated molecular properties. Calculations on several low‐lying states of butadiene are also reported where similar size‐inconsistency effects are found

Calculation of Electronic Coupling Matrix Elements for Ground and Excited State Electron Transfer Reactions: Comparison of the Generalized Mulliken–Hush and Block Diagonalization Methods

Two independent methods are presented for the nonperturbative calculation of the electronic coupling matrix element (Hab) for electron transfer reactions using ab initio electronic structure theory. The first is based on the generalized Mulliken–Hush (GMH) model, a multistate generalization of the Mulliken Hush formalism for the electronic coupling. The second is based on the block diagonalization (BD) approach of Cederbaum, Domcke, and co-workers. Detailed quantitative comparisons of the two methods are carried out based on results for (a) several states of the system Zn2OH2+ and (b) the low-lying states of the benzene–Cl atom complex and its contact ion pair. Generally good agreement between the two methods is obtained over a range of geometries. Either method can be applied at an arbitrary nuclear geometry and, as a result, may be used to test the validity of the Condon approximation. Examples of nonmonotonic behavior of the electronic coupling as a function of nuclear coordinates are observed for Zn2OH2+. Both methods also yield a natural definition of the effective distance (rDA) between donor (D) and acceptor (A) sites, in contrast to earlier approaches which required independent estimates of rDA, generally based on molecular structure data

A Theoretical Investigation of Several Low-Lying States of trans, trans-1,3,5-hexatriene

Results from ab initio calculations concerning several low-lying electronic states of trans,trans-1,3,5-hexatriene are presented and compared with experimental and previous theoretical results. The lowest excited singlet state is predicted to be the ¹B_u state, having essentially valencelike π → π* character. The nominally doubly excited 2¹A_g state is found to lie approximately 0.6-0.9 eV above the 1¹B_u state. Results are also presented for several Rydberg states. The implications of the present results for current parametrizations of semiempirical π molecular orbital schemes are discussed

A CASSCF Study of Various Rotamers of the Hexatriene Radical Cation

Results are presented from ab initio calculations on the ground and two low-lying excited states of the hexatriene radical cation in a variety of stable conformations of the electronic ground state of the molecule. We have performed Hartree-Fock geometry optimizations using the STO-3G and 6-31g basis sets and have performed vibrational analyses for all stable conformers in the 6-31G basis. In addition, we have performed geometry optimizations in both basis sets using CASSCF wave functions where the five π electrons are correlated. No new geometrical information is obtained at this level of treatment. Excitation energies to the two lowest-lying doublet π excited states for the six stable ground-state geometries were also calculated using CASSCF wave functions. These excitation energies are compared with previous experimental assignments of observed transitions in photolytically generated hexatriene radical cations

Tunneling through Weak Interactions: Comparison of Through-Space-, H-Bond-, and Through-Bond-Mediated Tunneling

Results from ab initio electronic structure theory calculations on model systems allow for the detailed comparison of tunneling through covalently bonded contacts, hydrogen bonds, and van der Waals contacts. Considerable geometrical sensitivity as well as an exponential distance dependence of the tunneling is observed for tunneling through various nonbonded contacts. However, the fundamental result from the present study is that at most a modest difference is observed between tunneling mediated by H-bonds and tunneling mediated by van der Waals contacts at typical distances for each type of interaction. These results are considered in relation to the pathways model of Beratan and Onuchic, and implications for understanding long-range tunneling in biological systems are discussed

On the Vertical and Adiabatic Excitation Energies of the 21A(g), State of trans-1,3-butadiene

The excitation energy to the 21Ag 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 21Ag state relative to the HOMO → LUMO excitation (11Bu) 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 ground-state geometry, the vertical excitation energies obtained by CASPT2 and Davidson-corrected MRSDCI for the 21Ag state differ by approximately 0.15 eV, but all of the methods predict that the 21Ag state has a lower 0−0 excitation energy than the 11Bu state. Possible reasons for the discrepancies between the various methods for the vertical excitation energy are discussed

Quasidegenerate Variational Perturbation Theory and the Calculation of First‐Order Properties from Variational Perturbation Theory Wave Functions

In previous work on the treatment of correlation in molecular systems we have applied a multireference version of second‐order Hylleraas variational perturbation theory. The choice made for the partitioning of H treated the interactions between the correlating functions to infinite order and gave the corrections to the wave function to first order. The method was shown to be accurate in many cases, but became less so when near degeneracies occurred between the reference energy and other eigenvalues of H0. In this article we introduce an effective Hamiltonian method that is analogous to variational perturbation theory, but which is significantly more accurate when near degeneracies are important. This quasidegenerate variational perturbation theory (QDVPT) is an explicitly multireference procedure and treats the entire reference space as a quasidegenerate space. A novel method for solving the QDVPT equations is introduced that avoids explicit construction of the effective Hamiltonian. As a result, the work involved in application of QDVPT is on the roder of that required for variational perturbation theory. We also present an approximate method for calculating first‐order atomic and molecular properties based on Hylleraas variational perturbation theory, multireference linearized coupled cluster, and QDVPT wave functions. The properties are calculated as derivatives of the energy with respect to the field strength. Construction of a one‐electron density matrix based on the energy derivative expression allows rapid evaluation of one‐electron properties. Results are presented and compared to full and truncated CI results. Good agreement is found in the cases examined

A Theoretical Investigation of Some Low-lying Singlet States of 1,3-butadiene

Results are presented from extensive ab initio calculations on several low-lying singlet states of cis- and trans-1,3-butadiene. The results indicate a qualitative difference between the cis and trans isomers for the lowest π → π* transition. For the cis isomer, the first excited singlet state of the same symmetry as the ground state is found to lie above the lowest π → π* transition, and we estimate that this is also the case for the trans isomer

Ab Initio Investigation of Several Low-lying States of All-trans Octatetraene

The results of ab initio calculations that examine vertical and nonvertical transitions to several low-lying states of all-trans-octatetraene are presented. It is found that the lowest vertical excitation is to a valence π → π* ¹B_u state, and the nominally doubly excited 2¹A_g state occurs approximately 0.4 eV higher at the geometry of the ground state. Using estimated excited-state equilibrium geometries, we find that the 2¹A_g state is indeed the lowest singlet excited state, having a 0-0 tarnsition energy of 4.15 eV. The 0-0 transition energy for the 1¹B_u state is calculated to be 4.56 eV. The present results are compared with past theoretical and experimental results