Ab initio characterization of electron transfer coupling in photoinduced systems: generalized Mulliken-Hush with configuration-interaction singles

To calculate electronic couplings for photoinduced electron transfer (ET) reactions, we propose and test the use of ab initio quantum chemistry calculation for excited states with the generalized Mulliken-Hush (GMH) method. Configuration-interaction singles (CIS) is proposed to model the locally excited (LE) and charge-transfer (CT) states. When the CT state couples with other high lying LE states, affecting coupling values, the image charge approximation (ICA), as a simple solvent model, can lower the energy of the CT state and decouple the undesired high-lying local excitations. We found that coupling strength is weakly dependent on many details of the solvent model, indicating the validity of the Condon approximation. Therefore, a trustworthy value can be obtained via this CIS-GMH scheme, with ICA used as a tool to improve and monitor the quality of the results. Systems we tested included a series of rigid, sigma-linked donor-bridge-acceptor compounds where "through-bond" coupling has been previously investigated, and a pair of molecules where "through-space" coupling was experimentally demonstrated. The calculated results agree well with experimentally inferred values in the coupling magnitudes (for both systems studied) and in the exponential distance dependence (for the through-bond series). Our results indicate that this new scheme can properly account for ET coupling arising from both through-bond and through-space mechanisms.     

Toward a molecular scale interpretation of excitation energy transfer in solvated bichromophoric systems

This paper presents a quantum-mechanical study of the intramolecular excitation energy transfer (EET) coupling in naphthalene-bridge-naphthalene systems in gas phase and in solution. ZINDO and TDDFT response schemes are compared using both an exact and an approximate solution. The approximate solution based on a perturbative approach uses the single chromophore properties to reconstruct the real system coupling thus neglecting possible through-bond effects which conversely are accounted for in the exact solution. The comparison of the results of the two approaches with the experiments allows a detailed analysis of the relative importance of through-bond and through-space effects as well as a more complete understanding of the modifications in the EET coupling with the size of the system, the chromophore-chromophore distance, and solvation.     

Synthesis and photophysical properties of steroid-linked porphyrin-fullerene hybrids

[structure: see text] The photophysical properties of porphyrin-linked fullerene hybrids have generated significant interest, and a number of these hybrids synthesized by this group and others have been extensively characterized with respect to energy and charge-transfer processes that take place upon photoexcitation. Present studies of steroid-linked dyads demonstrate the extent to which through-bond effects operate in these systems.     

Bacterial photosynthesis begins with quantum-mechanical coherence

In the antenna system of photosynthetic bacteria, pigments form circular aggregates whose excitations are excitons with quantum-mechanical coherence extending over many pigments. These excitons play crucial roles in light harvesting, storage, and excitation-energy transfer (EET). EET takes place rapidly to and/or from optically forbidden exciton states, without total transition dipole, within the antenna system and to the reaction center. Such EETs cannot be rationalized by F?rster's formula, the traditional theory on EET, because it allows EET only between optically allowed states. The coherence in the excitons seems to prohibit rapid EET on this formula. The bacteria overcome this difficulty by circumventing the coherence, using the effects of the physical size of an aggregate that is larger than the shortest distance between pigments in the donor and pigments in the acceptor. The shortest-distance pair therein cannot detect whether the aggregate has a nonvanishing total transition dipole or not, since the pair see effectively only the transition dipole on the other pigment in themselves. The transition dipole facilitates rapid EET even to and/or from optically forbidden exciton states. Such EETs have enabled us to develop a general formula for the rate constant of EET. This is a formula in the weak-interaction limit, and so is F?rster's formula, but it correctly takes into account the above size effect.     

Substitution effects on the absorption spectra of nitrophenolate isomers

Charge-transfer excitations highly depend on the electronic coupling between the donor and acceptor groups. Nitrophenolates are simple examples of charge-transfer systems where the degree of coupling differs between ortho, meta and para isomers. Here we report the absorption spectra of the isolated anions in vacuo to avoid the complications of solvent effects. Gas-phase action spectroscopy was done with two different setups, an electrostatic ion storage ring and an accelerator mass spectrometer. The results are interpreted on the basis of CC2 quantum chemical calculations. We identified absorption maxima at 393, 532, and 399 nm for the para, meta, and ortho isomer, respectively, with the charge-transfer transition into the lowest excited singlet state. In the meta isomer, this π-π* transition is strongly redshifted and its oscillator strength reduced, which is related to the pronounced charge-transfer character, as a consequence of the topology of the conjugated π-system. Each isomer's different charge distribution in the ground state leads to a very different solvent shift, which in acetonitrile is bathochromic for the para and ortho, but hypsochromic for the meta isomer.     

Three-dimensional through-space/through-bond delocalization in cyclophane systems: a molecule-in-molecule approach

In this article, we propose a simple strategy to identify the nature of excitonic couplings in a series of cyclophanedienes based on the "molecule-in-molecule" (MIM) theory. The contributions of charge-transfer (CT) exciton, unavailable by the commonly used supermolecular approach due to the inadequate basis set, can be unambiguously identified within this methodology. Combining the CT contributions calculated on the cyclophanedienes and the corresponding hypothetical molecules with tethers removed, one can infer the information on the relative importance of through-bond and through-space contributions in the low-lying excited states. Particularly, we discovered that the tether effect for the meta-linkage cyclophanedienes is crucial, whereas those for para-linkage cyclophanedienes are vanishingly small. The changes in the coupling between two moieties for both the six-membered meta-linkage and five-membered cyclophanedienes arise primarily from an increase in the through-bond charge-transfer component of the coupling (>70%). Within the MIM model, the delocalization pathway of the dimer in the excited state can be explained quantitatively by a CT exciton, which differs from the approach based on the conventional orbital interaction analysis.     

Communication: Tailoring the optical gap in light-harvesting molecules

Systematically varying the optical gap that is associated with charge-transfer excitations is an important step in the design of light-harvesting molecules. So far the guidance that time-dependent density functional theory could give in this process was limited by the traditional functionals' inability to describe charge-transfer excitations. We show that a nonempirical range-separated hybrid approach allows to reliably predict charge-transfer excitations for molecules of practically relevant complexity. Calculated absorption energies agree with measured ones. We predict from theory that by varying the number of thiophenes in donor-acceptor-donor molecules, the energy of the lowest optical absorption can be tuned to the lower end of the visible spectrum. Saturation sets in at about five thiophene rings.     

Solvatochromism of distyrylbenzene pairs bound together by [2.2]paracyclophane: evidence for a polarizable "through-space" delocalized state

A series of compounds were designed and synthesized to examine how through-space and through-bond electron delocalization respond to solvent effects. The general strategy involves the study of "dimers" of the distyrylbenzene chromophore held in close proximity by the [2.2]paracyclophane core and a systematic dissection of the chromophore into components with through-space and through-bond electronic delocalization. Steady state and time-resolved fluorescence spectroscopy in a range of solvents reveals a red-shift in emission and an increase in the intrinsic fluorescence lifetime for the emitting state in polar solvents when donor substituents are absent. We propose that through-space delocalization across the [2.2]paracyclophane core is more polarizable in the excited state, relative to the through-bond (distyrylbenzene based) excited state. When strong donors are attached to the distyrylbenzene chromophore, the charge transfer character of the distyrylbenzene-based excited state dominates fluorescence properties.     

Intervalence (charge-resonance) transitions in organic mixed-valence systems. Through-space versus through-bond electron transfer between bridged aromatic (redox) centers

Intervalence absorption bands appearing in the diagnostic near-IR region are consistently observed in the electronic spectra of mixed-valence systems containing a pair of aromatic redox centers (Ar(*)(+)/Ar) that are connected by two basically different types of molecular bridges. The through-space pathway for intramolecular electron transfer is dictated by an o-xylylene bridge in the mixed-valence cation radical 3(*)(+) with Ar = 2,5-dimethoxy-p-tolyl (T), in which conformational mobility allows the proximal syn disposition of planar T(*)(+)/T redox centers. Four independent experimental probes indicate the large through-space electronic interaction between such cofacial Ar(*)(+)/Ar redox centers from the measurements of (a) sizable potential splitting in the cyclic voltammogram, (b) quinonoidal distortion of T(*)(+)/T centers by X-ray crystallography, (c) "doubling" of the ESR hyperfine splittings, and (d) a pronounced intervalence charge-resonance band. The through (br)-bond pathway for intramolecular electron transfer is enforced in the mixed-valence cation radical 2a(*)(+) by the p-phenylene bridge which provides the structurally inflexible and linear connection between Ar(*)(+)/Ar redox centers. The direct comparison of intramolecular rates of electron transfer (k(ET)) between identical T(*)(+)/T centers in 3(*)(+) and 2a(*)(+)( )()indicates that through-space and through-bond mechanisms are equally effective, despite widely different separations between their redox centers. The same picture obtains for 3(*)(+) and 2a(*)(+)( )()from theoretical computations of the first-order rate constants for intramolecular electron transfer from Marcus-Hush theory using the electronic coupling elements evaluated from the diagnostic intervalence (charge-transfer) transitions. Such a strong coherence between theory and experiment also applies to the mixed-valence cation radical 7(*)(+), in which the aromatic redox S center is sterically encumbered by annulation.     

Assessment of a simple correction for the long-range charge-transfer problem in time-dependent density-functional theory

The failure of the time-dependent density-functional theory to describe long-range charge-transfer (CT) excitations correctly is a serious problem for calculations of electronic transitions in large systems, especially if they are composed of several weakly interacting units. The problem is particularly severe for molecules in solution, either modeled by periodic boundary calculations with large box sizes or by cluster calculations employing extended solvent shells. In the present study we describe the implementation and assessment of a simple physically motivated correction to the exchange-correlation kernel suggested in a previous study [O. Gritsenko and E. J. Baerends J. Chem. Phys. 121, 655 (2004)]. It introduces the required divergence in the kernel when the transition density goes to zero due to a large spatial distance between the "electron" (in the virtual orbital) and the "hole" (in the occupied orbital). A major benefit arises for solvated molecules, for which many CT excitations occur from solvent to solute or vice versa. In these cases, the correction of the exchange-correlation kernel can be used to automatically "clean up" the spectrum and significantly reduce the computational effort to determine low-lying transitions of the solute. This correction uses a phenomenological parameter, which is needed to identify a CT excitation in terms of the orbital density overlap of the occupied and virtual orbitals involved. Another quantity needed in this approach is the magnitude of the correction in the asymptotic limit. Although this can, in principle, be calculated rigorously for a given CT transition, we assess a simple approximation to it that can automatically be applied to a number of low-energy CT excitations without additional computational effort. We show that the method is robust and correctly shifts long-range CT excitations, while other excitations remain unaffected. We discuss problems arising from a strong delocalization of orbitals, which leads to a breakdown of the correction criterion.     

Solvent effects on isomerization and spectral properties of photochromic-switching diarythene derivatives in polar and apolar solutions

The photocyclization behavior and dynamic conformational transition of photochromic switches of diarythene derivatives in solutions are investigated by using the density functional theory (DFT) and molecular dynamics (MD) simulations. Three possible conformations, antiparallel (anti), parallel (para), and twist, for the open-ring isomers of 1,2-bis(2-methylbenzothiophene-3-yl)maleic anhydride are located. Both PCM-B3LYP/6-31G* calculations and MD simulations demonstrate that anti and twist open-ring isomers can interconvert freely in n-hexane and acetonitrile solutions at room temperature. The statistical ratio of twist to anti isomers from MD simulations is 2.09 in n-hexane and 1.07 in CH(3)CN, in qualitative agreement with those (1.18 in n-hexane and 1.05 in CH(3)CN) estimated from Arrhenius analysis of DFT activation energies. The solvent polarity has little influence on the isomerization of open-ring isomers in the ground state. Due to the evident charge transfer upon excitations, the solvent effects on the electronic structures and absorption spectra of low-lying excited states (S(1) and S(2)) are more significant. For such charge-transfer excited states, the long-range corrected functional CAM-B3LYP gives better agreement with the experimental spectra than B3LYP. The solvent polarity and polarization of the charge-transfer excited states are crucial for fabricating the novel functionalized photochromic molecular switches.     

Optical excitations of defects in realistic nanoscale silica clusters: comparing the performance of density functional theory using hybrid functionals with correlated wavefunction methods

Optical excitations of low energy silica (SiO(2))(4) clusters obtained by global optimization, as opposed to constructed by hand, are studied using a range of theoretical methods. By focusing on the lowest energy silica clusters we hope to capture at least some of the characteristic ways by which the dry surfaces of silica nanosystems preferentially terminate. Employing the six lowest energy (SiO(2))(4) cluster isomers, we show that they exhibit a surprisingly wide range of geometries, defects, and associated optical excitations. Some of the clusters show excitations localized on isolated defects, which are known from previous studies using hydrogen-terminated versions of the defect in question. Other clusters, however, exhibit novel charge-transfer excitations in which an electron transfers between two spatially separated defects. In these cases, because of the inherent proximity of the constituent defects due to the small cluster dimensions, the excitation spectrum is found to be very different from that of the same defects in isolation. Excitation spectra of all clusters were calculated using time-dependent density functional theory (TD-DFT) and delta-SCF DFT (DeltaDFT) methods employing two different hybrid density functionals (B3LYP and BB1K) differing essentially in the amount of incorporated Hartree-Fock-like exchange (HFLE). In all cases the results were compared with CASPT2 calculated values which are taken as a benchmark standard. In line with previous work, the spatially localized excitations are found to be well described by TD-DFT/B3LYP but which gives excitation energies that are significantly underestimated in the case of the charge-transfer excitations. The TD-DFT/BB1K combination in contrast is found to give generally good excitation energies for the lowest excited states of both localized and charge-transfer excitations. Finally, our calculations suggest that the increased quality of the predicted excitation spectra by adding larger amounts of HFLE is mainly due to an increased localization of the excited state associated with the elimination of spurious self-interaction inherent to (semi-)local DFT functionals.     

Studies of EPR parameters for Mn5+ -doped Li3PO4 and Li3VO4 crystals

The EPR parameters (zero-field splitting D and g factors g parallel, g perpendicular) of Mn5+ -doped Li3PO4 and Li3VO4 crystals are calculated from the complete high-order perturbation formulas based on a molecular orbital scheme for a 3d2 ion in tetragonal MX4 clusters. These formulas include not only the contribution coming from crystal-field excitations, but also that arising from charge-transfer excitations (which is discarded in crystal field theory). The calculated results are in reasonable agreement with the observed values. The contributions to EPR parameters coming from the charge-transfer excitations are comparable with those arising from the crystal-field excitations. It appears that for a high valence state 3dn ion in crystals, the reasonable explanations of EPR parameters should take the contributions due to both crystal-field and charge-transfer excitations into account.     

The ultrafast charge-transfer-to-solvent dynamics of iodide in tetrahydrofuran. 1. Exploring the roles of solvent and solute electronic structure in condensed-phase charge-transfer reactions

Although they represent the simplest possible charge-transfer reactions, the charge-transfer-to-solvent (CTTS) dynamics of atomic anions exhibit considerable complexity. For example, the CTTS dynamics of iodide in water are very different from those of sodide (Na-) in tetrahydrofuran (THF), leading to the question of the relative importance of the solvent and solute electronic structures in controlling charge-transfer dynamics. In this work, we address this issue by investigating the CTTS spectroscopy and dynamics of I- in THF, allowing us to make detailed comparisons to the previously studied I-/H2O and Na-/THF CTTS systems. Since THF is weakly polar, ion pairing with the counterion can have a substantial impact on the CTTS spectroscopy and dynamics of I- in this solvent. In this study, we have isolated "counterion-free" I- in THF by complexing the Na+ counterion with 18-crown-6 ether. Ultrafast pump-probe experiments reveal that THF-solvated electrons (e-THF) appear 380 +/- 60 fs following the CTTS excitation of "free" I- in THF. The absorption kinetics are identical at all probe wavelengths, indicating that the ejected electrons appear with no significant dynamic solvation but rather with their equilibrium absorption spectrum. After their initial appearance, ejected electrons do not exhibit any additional dynamics on time scales up to approximately 1 ns, indicating that geminate recombination of e-THF with its iodine atom partner does not occur. Competitive electron scavenging measurements demonstrate that the CTTS excited state of I- in THF is quite large and has contact with scavengers that are several nanometers away from the iodide ion. The ejection time and lack of electron solvation observed for I- in THF are similar to what is observed following CTTS excitation of Na- in THF. However, the relatively slow ejection time, the complete lack of dynamic solvation, and the large ejection distance/lack of recombination dynamics are in marked contrast to the CTTS dynamics observed for I- in water, in which fast electron ejection, substantial solvation, and appreciable recombination have been observed. These differences in dynamical behavior can be understood in terms of the presence of preexisting, electropositive cavities in liquid THF that are a natural part of its liquid structure; these cavities provide a mechanism for excited electrons to relocate to places in the liquid that can be nanometers away, explaining the large ejection distance and lack of recombination following the CTTS excitation of I- in THF. We argue that the lack of dynamic solvation observed following CTTS excitation of both I- and Na- in THF is a direct consequence of the fact that little additional relaxation is required once an excited electron nonadiabatically relaxes into one of the preexisting cavities. In contrast, liquid water contains no such cavities, and CTTS excitation of I- in water leads to local electron ejection that involves substantial solvent reorganization.     

Density functional calculations on electronic circular dichroism spectra of chiral transition metal complexes

Time-dependent density functional theory (TD-DFT) has for the first time been applied to the computation of circular dichroism (CD) spectra of transition metal complexes, and a detailed comparison with experimental spectra has been made. Absorption spectra are also reported. Various Co(III) complexes as well as [Rh(en)(3)](3+) are studied in this work. The resulting simulated CD spectra are generally in good agreement with experimental spectra after corrections for systematic errors in a few of the lowest excitation energies are applied. This allows for an interpretation and assignment of the spectra for the whole experimentally accessible energy range (UV/vis). Solvent effects on the excitations are estimated via inclusion of a continuum solvent model. This significantly improves the computed excitation energies for charge-transfer bands for complexes of charge +3, but has only a small effect on those for neutral or singly charged complexes. The energies of the weak d-to-d transitions of the Co complexes are systematically overestimated due to deficiencies of the density functionals. These errors are much smaller for the 4d metal complex. Taking these systematic errors and the effect of a solvent into consideration, TD-DFT computations are demonstrated to be a reliable tool in order to assist with the assignment and interpretation of CD spectra of chiral transition metal complexes.     

Identification of the matrix shift: a fingerprint for neutral neon complex?

Ar-NiCO and Ne-NiCO have been predicted as novel neutral noble gas charge-transfer complexes, with binding energies of 7.70 and 2.16 kcal/mol, respectively, by the highly correlated coupled-cluster singles and doubles including a perturbational estimate of triple excitations calculations. The calculated shifts in the Ni-C-O bending frequency are 48 and 36 cm(-1) for Ar-NiCO and Ne-NiCO, while the corresponding experimental matrix shifts are 46 and 36 cm(-1), respectively. The anharmonicity effects for these frequencies are verified to be very small. The interaction between a noble gas atom and NiCO is discussed through natural population analyses and the electron density difference map. We further examined the noble gas matrix effects on the geometrical structure and vibrational frequencies of NiCO by performing density functional theory calculations for the Ng31-NiCO (Ng = Ar, Ne, He) system. The present results will inspire the further experimental investigation on the complexes of noble gas and transition metal compounds generated in the matrix isolation experiments.     

Intramolecular charge-transfer state formation of 4-(N,N-dimethylamino)benzonitrile in acetonitrile solution: RISM-SCF study

Intramolecular charge-transfer (ICT) state formation of 4-(N,N-dimethylamino)benzonitrile in acetonitrile solution is studied by the reference interaction site model self-consistent field (RISM-SCF) method. Geometry optimizations are performed for each electronic state in solution with the complete-active-space SCF wave functions. Dynamic electron correlation effects are taken into account by using the multiconfigurational quasidegenerate perturbation theory. Two-dimensional free energy surfaces are constructed as the function of the twisting and wagging angles of the dimethylamino group for the ground and locally excited (LE) states. The calculated absorption and fluorescence energies are in good agreement with experiments. The validity of the twisted ICT (TICT) model is confirmed in explaining the dual fluorescence, and the possibility of the planar ICT model is ruled out. To examine the mechanism of the TICT state formation, a "crossing" seam between the LE and charge-transfer (CT) state surfaces is determined. The inversion of two electronic states occurs at a relatively small twisting angle. The effect of solvent reorganization is also examined. It is concluded that the intramolecular twisting coordinate is more important than the solvent fluctuation for the TICT state formation, because the energy difference between the two states is minimally dependent on the solvent configuration.     

Analysis of environment response effects on excitation energies within subsystem-based time-dependent density-functional theory

We analyze the ability of subsystem time-dependent density-functional theory (sTDDFT) to describe environmental response effects. To this end, we utilize the recently proposed “exact” version of sTDDFT relying on projection-based embedding (PbE), which so far was applied only for the special case of two subsystems. We confirm that PbE-sTDDFT in combination with supersystem bases yields results equivalent to those of supermolecular TDDFT calculations for systems solvated by many solvent molecules, using the previously studied system of methylene-cyclopropene⋯(H₂O)₁₇ as an example. By means of this exact reference embedding framework, we are able to disentangle solvent effects introduced in terms of the embedding potential from those caused by solvent response couplings, both for the PbE variant and for sTDDFT with approximate non-additive kinetic energy functionals. Furthermore, we show that the use of a monomer basis introduces significant errors for the environmental response contribution. Employing a virtual-orbital localization strategy on top of PbE-sTDDFT, we can also directly assess the impact of inter-subsystem charge-transfer excitations on the entire solvent effect, which turn out to play a significant role for the environmental response. Finally, we analyze the response effects introduced by the individual solvent molecules and their interdependence, and show that a simple, pair-wise additive correction for solvent response yields excellent results in the present example.     

Electron transfer and dynamic infrared-band coalescence: it looks like dynamic NMR spectroscopy, but a billion times faster

Broadening and coalescence of infrared bands can occur due to chemical exchange processes occurring on very fast, femtosecond-to-picosecond timescales. One such fast process of recent investigation is intramolecular electron transfer in transition-metal complexes with strong communication between electron-donor and -acceptor sites. The observation of partial coalescence of metal-carbonyl stretching bands in hexanuclear ruthenium mixed-valence complexes due to electron-transfer rates on the order of 10(11)-10(12) s(-1) is chronicled here. Several important advances have been made with the aid of dynamic infrared-band coalescence in these complexes, including the observation of dynamic solvent relaxation effects on electron-transfer rates, the determination of the equilibrium constant between charge-transfer isomers, and a reconsideration of the theory of electron transfer and delocalization in bridged, near-delocalized electron-transfer systems.