Time-dependent Density Functional Theory Investigation Research Articles

Structural and electronic properties of poly(fluorene–vinylene) copolymer and its derivatives: Time-dependent density functional theory investigation

The ground state and the lowest singlet excited-state geometries of poly-(9,9-dialkylfluorene-2,7-vinylene) copolymer or PFV and its derivatives (NH 2–FV) n , (CN–FV) n , (OMe–FV) n and (OH–FV) n ( n = 2–5) were investigated based on density functional theory (DFT) and time-dependent DFT using B3LYP functional. The ground state and the lowest singlet excited-state geometries of the oligomers were optimized at the B3LYP/6-31G ∗ and TD-B3LYP/SVP levels, respectively. The calculated ground state geometries favor the aromatic type structure, while the electronic excitations lead to quinoid type distortion, which exhibited a shortening of the inter-ring bonds (about 0.03 Å). Absorption and fluorescence energies were extrapolated to infinite chain length making use of their good linearity with respect to 1/ n. Extrapolated values of 2.19 eV for (FV) n was obtained by TD-B3LYP/TZVP method and 2.37, 2.11, 2.35 and 2.11 eV for its derivatives, (NH 2–FV) n , (CN–FV) n , (OMe–FV) n and (OH–FV) n , respectively. The predicted energy gaps of the copolymer derivatives were calculated and compared to available experimental data. Fluorescence energies are 1.78, 1.74, 2.00 and 1.73 eV and the predicted radiative lifetime are 0.6, 1.0, 0.8 and 1.0 ns. for (FV) n , (CN–FV) n , (OMe–FV) n and (OH–FV) n , respectively. These fundamental structural and electronic informations can be useful in designing of novel conducting polymer materials.

TD-DFT investigation on the electronic spectra of novel N-methylmaleimides linked with indolizine ring system

The major electronic absorption features in visible region were computationally investigated for a series of novel N-methylmaleimide derivatives. The newly synthesized compounds through the reaction of indolizines with N-methylmaleimides exhibited their maxima ranging 587–634 nm in solution at room temperature. Time dependent density functional theory (TD-DFT) calculations were performed in order to elucidate their structure–color relationship, as well as to assess its performance using a variety of exchange-correlation (XC) functionals and basis sets. 4-(Indolizin-3-yl)-1-methyl-2,5-dioxo-1 H-pyrrole-3-carbonitrile (referred to 3a hereafter), a representative of the new compounds, was analyzed in detail on its intramolecular push–pull electronic structure. As a consequence of systematic evaluation of computational strategies for 3a, we found that the theoretical λ max obtained by PCM-TD-DFT/6-31+G(d, p)//DFT/6-311G(2d, 2p) level of theory, which was consistently employed throughout this study, has converged within 2 nm deviation from λ max of the most elaborated level considered. Among some of the molecules with near-planarity structure, unusual discrepancies between the theoretical and the experimental λ max were observed, which should be attributed to the well-known TD-DFT limitation to describe multi-configurational or charge transfer (CT) excitations.

Time-Dependent Density Functional Theory Investigations on the Excited States of Ru(II)-Dye-Sensitized TiO2 Nanoparticles: The Role of Sensitizer Protonation

We performed fully first principles quantum mechanical calculations of the ground- and excited-state properties of the [cis-(NCS)2-Ru(II)-bis(2,2‘-bipyridine-4,4‘-dicarboxylate)] dye, N719, adsorbed onto a model TiO2 nanoparticle. Our study confirms an indirect electron injection mechanism for Ru(II) dyes on TiO2 and indicates a remarkable effect of dye protonation on the electronic properties of N719-sensitized TiO2 nanoparticles. We find that two different electron injection mechanisms (adiabatic and nonadiabatic) may be present in DSSCs employing dyes carrying a different number of protons. Despite such differences, the absorption spectra corresponding to strongly and weakly coupled dye/TiO2 excited states are remarkably similar, so that a discrimination of the two electron injection regimes does not appear to be feasible based on inspection of the absorption spectra.

Time-dependent density functional theory investigation of the absorption and emission spectra of a cyanine dye

Density and time-dependent density functional theory have been used to simulate the vibronic structure of the emission and absorption spectra of a typical trimethine cyanine dye. This approach combines the BH and HLYP exchange-correlation functional with the Doktorov scheme to evaluate the Franck–Condon factors. The absorption and emission spectra present a dominant band and a shoulder, which nicely reproduce the experimental data. The theoretical calculations demonstrate that the simplicity of the shape results from rather small geometry relaxations in the first excited state, though many vibrational normal modes contribute to it.

Quantum Chemical Study on the Circular Dichroism Spectra and Specific Rotation of Donor−Acceptor Cyclophanes

The structures of donor,acceptor-substituted cyclophanes were optimized by DFT and MP2 methods and compared with the X-ray crystallographic structures. The electronic circular dichroism (CD) spectra of these chiral cyclophanes were simulated by time dependent density functional theory (TD-DFT) with several functionals including different amounts of "exact" Hartree-Fock exchange. The experimental oscillator and rotatory strengths were best reproduced by the BH-LYP/TZV2P method. The specific rotation and vibrational circular dichroism (VCD) spectra were also calculated at the BH-LYP/aug-cc-pVDZ and B3-LYP/6-31G(d) levels, respectively, and compared with the experimental data. Better performance was obtained with the ECD, rather than the specific rotation or the VCD spectral calculations in view of the computation time and accuracy for the determination of absolute configuration (AC). The exciton coupling model can be applied only for the cyclophanes without CT-character. However, the split pattern found in the experiment does not appear to originate from a simple two-transition coupling, indicating that this method should be applied with caution to the AC determination. This conclusion was supported by the TD-DFT investigations of the transition moments and the roles of excited-state electronic configuration associated with these split bands. Cyclophanes with donor-acceptor interactions showed Cotton effects at the CT band and couplets at the 1La and 1Lb bands. Although the degree of charge transfer between the rings is very small, as revealed by a Mulliken-Hash analysis, the split Cotton effects are due to a large separation in energy of the donor and acceptor orbitals. The effect of the distance and angle between the donor and acceptor moieties in model (intermolecular) CT complexes on the calculated CD spectra was also studied and compared with those obtained for various paracyclophanes.

Time-dependent density functional theory investigation of the absorption, fluorescence, and phosphorescence spectra of solvated coumarins

Using time-dependent density functional theory (TD-DFT) and the polarizable continuum model, we have computed the electronic transitions of a large panel of coumarin dyes in their enol, keto, cationic, and anionic forms. Several processes have been studied: absorption, fluorescence, 0-0 phosphorescence, and triplet-triplet excitations. For each process, detailed comparison with experimental data has been carried out. Using the PBE06-31+G(d) scheme, it turns out that for a given electronic transition the experimental shifts resulting from the substitution of the coumarin core are nicely reproduced. Indeed, once a simple statistical correction is applied, the mean absolute errors on the absorption and fluorescence wavelengths are limited to 8 nm (0.09 eV) and 9 nm (0.07 eV), respectively. A valuable correlation between the experimental and theoretical phosphorescence auxochromic displacements has also been unravelled. The differences between the wavelengths of the various electronic processes of a given dye tend to be fairly predicted, especially for the fluorescence-phosphoresence shifts that are strongly overestimated by TD-DFT.

TD-DFT investigation on the low-lying excited states of spiro-bithiophene

Modifications of the optical properties and charge mobility of spiro-bithiophene (SCPDT) were investigated by time-dependent density functional theory (TD-DFT). Geometry optimizations have been performed for the ground state and excited state of bithiophene (BT), 4H-cyclopenta[2,1-b:3,4-b′]dithiophene (CPDT) and SCPDT. Vertical excitations and emission transition energies have been calculated. The computed vertical and emission transition energies of BT and CPDT are in good agreement with the experimental data. Compared to CPDT and BT, SCPDT is expected to be an effective EL material by considering that smaller reorganization energy is presented and fluorescence quantum efficiency of non-spiro isolated fragment is preserved in the molecule with spiro-structure.

Surface-Enhanced Raman Scattering of Pyrazine at the Junction between Two Ag20 Nanoclusters

In this work we present a detailed time-dependent density functional theory (TDDFT) investigation of the absorption and Raman spectra of a pyrazine molecule located at the junction between two Ag20 clusters. Surface-enhanced Raman scattering enhancements of the order of 10(6) have been found for the junction system, which are similar to enhancements of 10(5) found for individual silver nanoparticles. Surprisingly, the chemical enhancement is found to account for as much as 10(5), suggesting that this mechanism might be more important than previously believed, in particular for nanoparticle aggregates. Moreover, TDDFT calculations suggest that unlike larger nanoparticles, the junction between small Ag20 tetrahedral clusters does not provide an electromagnetic "hot spot".

Absorption Spectra of Caffeic Acid, Caffeate and Their 1:1 Complex with Al(III): Density Functional Theory and Time-Dependent Density Functional Theory Investigations

The UV-visible absorption spectra of caffeic acid, caffeate and of the predominant complex obtained in the presence of aluminum ion (1:1 stoichiometry) have been simulated by using the time-dependent density functional theory (TD-DFT) technique, taking into account solvent effects. Whereas the use of the B3LYP hybrid XC functional with the 6-31+G(d,p) basis set allows us to reproduce fairly well the essential features of the experimental spectra of caffeic acid and caffeate, it is necessary to introduce an effective core potential to properly describe the aluminum ion and its environment and to obtain a good agreement between theoretical and experimental spectra of the 1:1 complex. The ligand presents two potential complexing sites in competition. The results of our calculations show that the aluminum ion coordinates preferentially at the level of the catecholate group, and the [Al(H(2)O)(4)(CA)], [Al(H(2)O)(3)(OH)(CA)](-) and [Al(H(2)O)(4)(HCA)](+) complexed forms could coexist in aqueous solution at pH = 5.

A time-dependent density functional theory investigation on the nature of the electronic transitions involved in the nonlinear optical response of [Ru(CF3CO2)3T] (T = 4′-(C6H4-p-NBu2)-2,2′:6′,2″-terpyridine)

We report a theoretical study based on density functional theory (DFT) and time-dependent DFT (TDDFT) calculations on the nature and role of the absorption bands involved in the nonlinear optical response of the complexes [Ru(CF3CO2)3T] (T = T1, T2; T1 = 4'-(C6H4-p-NBu2)-2,2':6',2''-terpyridine, T2 = 4'-(C6H4-p-NMe2)-2,2':6',2''-terpyridine). Geometry optimizations, performed without any symmetry constraints, confirm a twisting of the -C6H4-p-NBu2 moiety with respect to the plane of the chelated terpyridine. Despite this lack of strong pi interaction, TDDFT excited states calculations of the electronic spectrum in solution provide evidence of a relevant role of the NBu2 donor group in the low-energy LMCT band at 911 nm. Calculations also show that the two bands at higher energy (508 and 455 nm) are not attributable only to LMCT and ILCT transitions but to a mixing of ILCT/MLCT and ILCT/pi-pi* transitions, respectively. The 911 nm LMCT band, appearing at lower wavelength of the second harmonic (670 nm) of the EFISH experiment, controls the negative value of the second-order NLO response. This is confirmed by our calculations of the static component beta0(zzz) of the quadratic hyperpolarizability tensor, showing a large positive value. In addition we have found that the increase of the dipole moment upon excitation occurs, in all the characterized transitions, along the dipole moment axis, thus explaining why the EFISH and solvatochromic experimental values of the quadratic hyperpolarizability agree as sign and value.

Time-Dependent Density Functional Theory Investigation of Electric Field Effects on Absorption Spectra of Meso−Meso-Linked Zinc Porphyrin Arrays: Role of Charge-Transfer States

By using time-dependent density functional theory, we calculated the transition energies of a zinc porphyrin monomer and its meso-meso-linked arrays. In line with the prediction of the molecular exciton model, the calculated splitting energy of the Soret band increased as the number of linked porphyrins increased. We then examined how the transition energies of the dimer array were shifted by an applied electric field. For reproduction of an electroabsorption spectrum (EA), i.e., the field-induced change in absorption intensity, a model Hamiltonian constructed from five states is proposed. It is concluded for the dimer that the field-induced coupling between the lower-energy Soret band Se and the lower-lying ionic character (charge-transfer) states is responsible for the experimentally observed blue shift of Se as well as the second-derivative profile in the EA spectrum.

Time-Dependent Density Functional Theory Investigation of Electronic Excited States of Tetraoxaporphyrin Dication and Porphycene

The electronic ground state and the singlet vertical excited states of tetraoxaporphyrin dication (TOPDC) and porphycene have been investigated by using time-dependent density functional theory (TDDFT) for the first time. The solvation effects on the excitation energies for TOPDC in 96% H2SO4 and porphycene in 2-methyltetrahydrofuran are taken into account by using the polarized continuum model (PCM). The TDDFT-PCM computed results show an obvious red shift of the excitation energies of the B (Soret) bands, leading to a much better agreement with the UV/vis absorption spectra in solutions than the previous semiempirical calculations in vacuo.

Rational classification of a series of aromatic donor–acceptor systems within the twisting intramolecular charge transfer model, a time-dependent density-functional theory investigation

The goal of this paper is to rationalize the fluorescence activity, experimentally observed for 21 molecules of the same family as the 4-(N,N-dimethyl)anilines, based on their potential energy surfaces calculated within the twisting intramolecular charge transfer model. A classification in four groups is proposed according to the sign of two parameters, ΔEgap, characterizing the energy difference between the vertical locally and charge transfer excited states, and ΔE1S (or ΔẼ1S for pretwisted systems), representing the energy gain of the charge transfer excited state with a perpendicular conformation compared to the first vertical excited state. In this study, the time-dependent density-functional theory has been used to calculate the potential energy surfaces of the ground and excited states along the twisting angle. Computed excitation energies and optimized ground state geometries have been obtained with both B3LYP and MPW1PW91 functionals using a 6-311+G(2d,p), and a 6-31G(d) basis set, respectively. From this study, it follows that ΔEgap and ΔE1S are the main parameters necessary to understand the fluorescence activity of these molecules. The fact that the same fluorescence activity is observed for the members of each group (or subcategory for the particular case of group II), reveals the underlying twisting mechanism as a common process for all the investigated molecules, which explains their experimental dual and nondual emission.

A time-dependent density-functional theory investigation of the fluorescence behavior of related cyano and di-cyano isomers of 4-( N, N-dimethylamino) benzonitrile

We present a time-dependent density-functional theory investigation of the absorption and emission energies for 2-CDMA, 3,5-DCDMA, and 3,4-DCDMA. Ground state geometries were optimized using density functional theory (DFT). Using the TICT (twisting intramolecular charge transfer) model to investigate the potential energy surface, we find that the non-dual fluorescence experimentally observed for all systems is explained by the presence of a large energy gap between the first and the second excited states. Our previous classification [submitted to JACS] established within the TICT model for this family of compounds also holds for the present systems.

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.

Time-dependent density-functional theory investigation of the formation of the charge transfer excited state for a series of aromatic donor–acceptor systems. Part II

TDDFT singlet excitation energies calculations have been performed for a series of donor–acceptor para-substituted N,N-dimethyl-anilines (4DMAB-CHO, 4DMAB-COMe, 3DMAB-CHO, 3DMAB-COMe, 4DMAB-COOH, 4DMAB-COOMe, 4DMAB-CONH2, 4DMAB-CON(CH3)2, and DMAPY) using both B3LYP and MPW1PW91 functionals with a 6-311*(2p,d) basis set. The aim of this study is to investigate the influence of the variation of the acceptor group on the fluorescence behavior of these molecules. This work is a complementary investigation to part I [J. Chem. Phys. 117, 4146 (2002), preceding paper], where variation of the donor group has been studied. Ground-state geometries were optimized using density-functional theory (DFT) with both B3LYP and MPW1PW91 functionals combined with a 6-31G(d) basis set. For all molecules, the potential energy surface has been investigated following the twisting intramolecular charge transfer (TICT) model proposed in the literature as a possible mechanism to explain the fluorescence behavior. Computed vertical absorption energies using the MWP1PW91 and B3LYP functionals compare within 0.02 and −0.09 eV in average with gas-phase experimental data (4DMAB-COMe and 4DMAB-COOMe). Almost all para compounds are predicted to be dual fluorescent within the TICT model, in agreement with experiments. The present calculations predict 4DMAB-CONH2 to be dual fluorescent in nonpolar solvent in disagreement with experimental results. For meta compounds, the literature is sparse and no fluorescence spectra have been reported for these systems. Our results indicate that these molecules should exhibit only one band in the fluorescence spectra. Our calculations reinforce the validity of the TICT model as a possible mechanism to explain the fluorescence activity of these donor–acceptor systems.

Time-dependent density-functional theory investigation of the formation of the charge transfer excited state for a series of aromatic donor–acceptor systems. Part I

Singlet excitation energies for a series of acceptor para-substituted N,N-dimethyl-anilines that are dual (4DMAB-CN, 3M4MAB-CN, MHD) and nondual (4AB-CN, 3M4AB-CN, 4MAB-CN, 3M4DMAB-CN, HHD, and MMD) fluorescent have been performed using the TDDFT method. The aim of this study is to investigate the influence of changing donor groups as well as the addition of methyl groups to the benzene moiety, on the fluorescence behavior of these molecules. Calculations of excitation energies have been performed with both B3LYP and MPW1PW91 functionals using a 6-311*(2p,d) (Bg) basis set. For all systems, ground-state geometries were optimized using density-functional theory with the Becke three parameter Lee–Yang–Parr functional combined with a 6-31G(d) (Sm) basis set. In addition, 4AB-CN, 4DMAB-CN, and MMD ground-state geometry has also been optimized using the MPW1PW91 functional with the Sm basis set. For all molecules, the potential energy surface (PES) has been investigated following the twisting intramolecular charge transfer (TICT) model proposed in the literature as a possible mechanism to explain the fluorescence behavior. Both 4AB-CN and HHD molecules have been computed to be nondual fluorescent in full agreement with experimental spectra. The single band observed in the gas-phase fluorescence spectra of 3M4DMAB-CN, and MMD is clearly understood by the form of the PES of the charge transfer excited state that presents a minimum for the perpendicular structure. The qualitative picture of the PES along the twisting angle is in full agreement with experimental observations. The dual fluorescence of 4DMAB-CN and 3M4MAB-CN is explained, within the TICT model, by a double mechanism proposed by Serrano et al. [J. Am. Chem. Soc. 117, 3189 (1995)], that involves the presence of two low-lying states close enough in energy. The nondual fluorescence of 4MAB-CN is explained by the height of the energy barrier (larger than for 4DMAB-CN and 3M4MAB-CN). Finally, the dual fluorescence of the MHD molecule can be fully understood by a double mechanism within the TICT model. 3M4AB-CN is computed nondual fluorescent like 4AB-CN and HHD, but no experimental data has been reported in the literature so far. Our calculations give new evidence in favor of the TICT model as an explanation for the occurrence of dual fluorescence.

Time-dependent density-functional theory investigation of excitation spectra of open-shell molecules

Time-dependent density-functional theory is developed for open-shell molecular systems and implemented in the post-deMon program, DynaRho (version 2pX). In case studies, this time-dependent density-functional theory is applied to study excitation energies and oscillator strengths of open-shell molecules, three neutral molecules (BeH, BeF, CN) and three positive ions ( CO +, N 2 +, CH 2 O +). To our knowledge, our calculated excitation spectra of such open-shell molecules are the first applications of time-dependent density-functional theory to such open-shell systems, except for the recent calculation of the lowest two excitation energies (without oscillator strengths) of a few open-shell molecules [S. Hirata, M. Head-Gordon, Chem. Phys. Lett. 302 (1999) 375] and the calculation of the potential energy surfaces of excited states of the open-shell species PO [A. Spielfiedel, N.C. Handy, Phys. Chem. Chem. Phys. 1 (1999) 2401]. The present calculations of the open-shell molecules show that time-dependent density-functional theory can treat open-shell systems fairly well, and the present calculated excitation energies with both LSDxc/TDLSDxc and LB94xc/TDLSDxc functionals are comparable with traditional ab initio methods.