Dependence of charge transfer reorganization energy on carrier localisation in organic molecular crystals

Taking the organic molecular material dithiophene-tetrathiafulvalene (DT-TTF) as an example of a high mobility organic molecular material, we use density functional calculations to calculate the dependency of the reorganization energy associated with charge carrier transport on: (i) the geometric and electronic responsiveness of the local molecular crystal environment, and, (ii) the local spatial extent of the charge carrier. We find that in our most realistic extended models the charge transfer reorganization energy is strongly dependent on carrier localization. In particular, whereas highly localized carriers are found to be highly susceptible to their charge transfer efficiency being affected by changes in the local crystal environment, more delocalized carriers are better able to maintain their low reorganization energies. Considering that maintaining a relatively small charge transfer reorganization energy magnitude is an important factor in achieving high carrier mobilities, we suggest that those materials better able to sustain carriers with short-range thermally resistant intermolecular delocalisation should be sought for device applications.     

On the mechanism of charge transport in pentacene

Terahertz transient conductivity measurements are performed on pentacene single crystals, which directly demonstrate a strong coupling of charge carriers to low frequency molecular motions with energies centered around 1.1 THz. We present evidence that the strong coupling to low frequency motions is the factor limiting the conductivity in these organic semiconductors. Our observations explain the apparent paradox of the "bandlike" temperature dependence of the conductivity beyond the validity limit of the band model.     

Intramolecular vibrational energy redistribution in bridged azulene-anthracene compounds: ballistic energy transport through molecular chains

Intramolecular vibrational energy flow in excited bridged azulene-anthracene compounds is investigated by time-resolved pump-probe laser spectroscopy. The bridges consist of molecular chains and are of the type (CH(2))(m) with m up to 6 as well as (CH(2)OCH(2))(n) (n=1,2) and CH(2)SCH(2). After light absorption into the azulene S(1) band and subsequent fast internal conversion, excited molecules are formed where the vibrational energy is localized at the azulene side. The vibrational energy transfer through the molecular bridge to the anthracene side and, finally, to the surrounding medium is followed by probing the red edge of the azulene S(3) absorption band at 300 nm and/or the anthracene S(1) absorption band at 400 nm. In order to separate the time scales for intramolecular and intermolecular energy transfer, most of the experiments were performed in supercritical xenon where vibrational energy transfer to the bath is comparably slow. The intramolecular equilibration proceeds in two steps. About 15%-20% of the excitation energy leaves the azulene side within a short period of 300 fs. This component accompanies the intramolecular vibrational energy redistribution (IVR) within the azulene chromophore and it is caused by dephasing of normal modes contributing to the initial local excitation of the azulene side and extending over large parts of the molecule. Later, IVR in the whole molecule takes place transferring vibrational energy from the azulene through the bridge to the anthracene side and thereby leading to microcanonical equilibrium. The corresponding time constants tau(IVR) for short bridges increase with the chain length. For longer bridges consisting of more than three elements, however, tau(IVR) is constant at around 4-5 ps. Comparison with molecular dynamics simulations suggests that the coupling of these chains to the two chromophores limits the rate of intramolecular vibrational energy transfer. Inside the bridges the energy transport is essentially ballistic and, therefore, tau(IVR) is independent on the length.     

The effect of substitution on reorganization energy and charge mobility in metal free phthalocyanine

To gain insight into how the electronic properties of discotic organic materials may be modified through substitution, the reorganization energy and the charge mobility of metal free phthalocyanine, and of several mono-substituted derivatives, are studied by electronic structure methods. It is found that the reorganization energy of phthalocyanine is not significantly changed by substitution on an outer phenyl ring, but is more strongly influenced when the inner crown amine ring is substituted. The relationship between reorganization energy and substituent is studied through the use of; substituent constant, HOMO energy, and geometry relaxation. The computed charge mobility shows stronger relationship to coupling matrix element than reorganization energy. A hybrid computational screening method in which the reorganization energy is calculated at the DFT level and the coupling matrix element is calculated at the AM1 level shows good predicting power for trends in charge mobility at reduced computational expense.     

Probing inhomogeneous vibrational reorganization energy barriers of interfacial electron transfer

An atomic force microscopy (AFM) and confocal Raman microscopy study of the interfacial electron transfer of a dye-sensitization system, i.e., alizarin adsorbed upon TiO(2) nanoparticles, has revealed the distribution of the mode-specific vibrational reorganization energies encompassing different local sites ( approximately 250-nm spatial resolution). Our experimental results suggest inhomogeneous vibrational reorganization energy barriers and different Franck-Condon coupling factors of the interfacial electron transfer. The total vibrational reorganization energy was inhomogeneous from site to site; specifically, mode-specific analyses indicated that energy distributions were inhomogeneous for bridging normal modes and less inhomogeneous or homogeneous for nonbridging normal modes, especially for modes far away from the alizarin-TiO(2) coupling hydroxyl modes. The results demonstrate a significant step forward in characterizing site-specific inhomogeneous interfacial charge-transfer dynamics.     

The kinetic energy of molecular charge distributions and molecular stability

This paper examines the relationship between the topographical features of a molecular charge distribution and the kinetic energy of the system. Specifically, the spatial contributions to the kinetic energy are related to the Laplacian of the total charge density and to the gradients of the natural-orbital densities. It is concluded that a necessary requirement for molecular stability is the existence of a net negative curvature for the molecular charge distribution in the internuclear region. It is shown that the charge density accumulated in the internuclear region of a stable molecule is distributed in such a way as to keep the accompanying increase in the kinetic energy to a minimum. A comparison of the contributions to the kinetic energy from the atomic and molecular charge distributions indicates that in the formation of a stable molecule the contribution from the molecular charge density in the binding region is decreased relative to that of the atoms.     

Spatially resolved vibrational energy transfer in molecular monolayers

We have shown that it is possible to input heat to one location of a molecule and simultaneously measure its arrival in real time at two other locations, using an ultrafast flash-thermal conductance technique. A femtosecond laser pulse heats an Au layer to approximately 800 degrees C, while vibrational sum-frequency generation spectroscopy (SFG) monitors heat flow into self-assembled monolayers (SAMs) of organic thiolates. Heat flow into the SAM creates thermally induced disorder, which decreases the coherent SFG signal from the CH-stretching transitions. Recent improvements in the technique are described, including the use of nonresonant background-suppressed SFG. The improved apparatus was characterized using alkanethiolate and benzenethiolate SAMs. In the asymmetric 2-methyl benzenethiolate SAM, SFG can simultaneously monitor CH-stretching transitions of both phenyl and methyl groups. The phenyl response to flash-heating occurs at least as fast as the 1 ps time for the Au surface to heat. The methyl response has a faster portion similar to the phenyl response and a slower portion characterized by an 8 ps time constant. The faster portions are attributed to disordering of the methyl-substituted phenyl rings due to thermal excitation of the Au-S adbonds. The slower portion, seen only in the methyl SFG signal, is attributed to heat flow from the metal surface into the phenyl rings and then to the methyl groups.     

Partial Hessian vibrational analysis: the localization of the molecular vibrational energy and entropy

The partial Hessian vibrational analysis (PHVA), in which only a subblock of the Hesssian matrix is diagonalized to yield vibrational frequencies for partially optimized systems, is extended to the calculation of vibrational enthalpy and entropy changes for chemical reactions. The utility of this method is demonstrated for various deprotonation reactions by reproducing full HVA values to within 0.1–0.4 kcal/mol, depending on the number atoms included in the PHVA. When combined with the hybrid effective fragment potential method [Gordon MS, et al. (2001) J Phys Chem A 105:293–307], the PHVA method can provide (harmonic) free-energy changes for localized chemical reactions in very large systems. Received: 21 September 2001 / Accepted: 30 October 2001 / Published online: 22 March 2002     

Influence of functional groups on charge transport in molecular junctions

Using density functional theory (DFT), we analyze the influence of five classes of functional groups, as exemplified by NO(2), OCH(3), CH(3), CCl(3), and I, on the transport properties of a 1,4-benzenedithiolate (BDT) and 1,4-benzenediamine (BDA) molecular junction with gold electrodes. Our analysis demonstrates how ideas from functional group chemistry may be used to engineer a molecule's transport properties, as was shown experimentally and using a semiempirical model for BDA [Nano Lett. 7, 502 (2007)]. In particular, we show that the qualitative change in conductance due to a given functional group can be predicted from its known electronic effect (whether it is sigma/pi donating/withdrawing). However, the influence of functional groups on a molecule's conductance is very weak, as was also found in the BDA experiments. The calculated DFT conductances for the BDA species are five times larger than the experimental values, but good agreement is obtained after correcting for self-interaction and image charge effects.     

Transition from IVR limited vibrational energy transport to bulk heat transport

In a previous paper [M. Schade, P. Hamm, Vibrational energy transport in the presence of intrasite vibrational energy redistribution, J. Chem. Phys. 131 (2009) 044511], it has been shown that on ultrashort length and time scales, the speed of vibrational energy transport along a molecular chain is limited by intrasite vibrational relaxation rather than the actual intersite propagation. However, since intrasite vibrational relaxation is length independent, the intersite propagation rate is expected to become rate-limiting at some length scale, where propagation approaches the bulk limit. In the present paper, we investigate the transition between both regimes. The response of different types of modes may be very different at early times, depending on how much they contribute directly to energy transport. Surprisingly though, when averaging the energy content over all vibrational modes of the various chain sites, the complexity of the intrasite vibrational relaxation process is completely hidden so that energy transport on the nanoscale can be described by an effective propagation rate, that equals the bulk value, even at short times.     

Theoretical study of substitution effects on molecular reorganization energy in organic semiconductors

Chemical substitutions are powerful molecular design tools to enhance the performance of organic semiconductors, for instance, to improve solubility, intermolecular stacking, or film quality. However, at the microscopic level, substitutions in general tend to increase the molecular reorganization energy and thus decrease the intrinsic charge-carrier mobility. Through density functional theory calculations, we elucidate strategies that could be followed to reduce the reorganization energy upon chemical substitution. Specific examples are given here for hole-transport materials including indolo-carbazoles and several triarylamine derivatives. Through decomposition of the total reorganization energy into the internal coordinate space, we are able to identify the molecular segment that provides the most important contributions to the reorganization energy. It is found that when substitution reduces (enhances) the amplitude of the relevant frontier molecular orbital in that segment, the total reorganization energy decreases (increases). In particular, chlorination at appropriate positions can significantly reduce the reorganization energy. Several other substituents are shown to play a similar role, to a greater or lesser extent.     

Efficient charge transport along phenylene-vinylene molecular wires

We have studied the motion of charge carriers along isolated phenylene-vinylene (PV) chains using a combination of experimental and theoretical methods. The conductive properties of positive charges along PV chains in dilute solution were studied by using the pulse-radiolysis time-resolved microwave conductivity (TRMC) technique. This technique enables the measurement of high-frequency (tens of GHz) charge carrier mobilities along isolated PV chains without the use of electrodes. The charge carrier mobility along PV chains with finite and infinite length was studied theoretically by charge transport simulations with parameters from density functional theory (DFT) calculations. The high-frequency charge carrier mobility is found to depend strongly on the conjugation length of the PV chains and is found to increase both with increasing length of the PV chain and with increasing conjugation fraction. The experimental results are in good agreement with the calculated results. On the basis of this combined experimental and theoretical study an intrachain charge carrier mobility of a few tens of cm2/Vs is expected for an infinitely long PV chain without conjugation breaks.     

The reorganization energy of electron transfer in nonpolar solvents: molecular level treatment of the solvent

The intermolecular electron transfer in a solute pair consisting of pyrene and dimethylaniline is investigated in a nonpolar solvent, n-hexane. The earlier elaborated approach [M. Tachiya, J. Phys Chem. 97, 5911 (1993)] is used; this method provides a physically relevant background for separating inertial and inertialess polarization responses for both nonpolarizable and polarizable molecular level simulations. The molecular-dynamics technique was implemented for obtaining the equilibrium ensemble of solvent configurations. The nonpolar solvent, n-hexane, was treated in terms of OPLS-AA parametrization. Solute Lennard-Jones parameters were taken from the same parametrization. Solute charge distributions of the initial and final states were determined using ab initio level [HF/6-31G(d,p)] quantum-chemical calculations. Configuration analysis was performed explicitly taking into account the anisotropic polarizability of n-hexane. It is shown that the Gaussian law well describes calculated distribution functions of the solvent coordinate, therefore, the rate constant of the ET reaction can be characterized by the reorganization energy. Evaluated values of the reorganization energies are in a range of 0.03-0.11 eV and significant contribution (more then 40% of magnitude) comes from anisotropic polarizability. Investigation of the reorganization energy lambda dependence on the solute pair separation distance d revealed unexpected behavior. The dependence has a very sharp peak at the distance d=7 A where solvent molecules are able to penetrate into the intermediate space between the solute pair. The reason for such behavior is clarified. This new effect has a purely molecular origin and cannot be described within conventional continuum solvent models.     

Investigating charge transport in molecular switches with neural networks

The control of charge transport on a polymer chain by impurity molecules working as switches is studied. Charge propagation is estimated using a backpropagation neural network approach. The supervised learning is accomplished using theoretical results in which the chain is modeled by a tight-binding Hamiltonian extended to include the effects of an external electric field. The charge transport through the sites that work like a switch is analyzed by the numerical integration of the equations of motion. For a donor–acceptor pair of impurities, we found that the chain offers a wide range of devices, from simple switches to perfect molecular rectifiers. The influence of the parameters of the molecules on the charge transport, the role of the length of separation between the sites where the impurity molecules bond, as well as the changes they must undergo to characterize each kind of molecular switch are determined. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1060–1066, 1999     

The role of molecular recognition in charge transport properties of doped polyaniline

Molecular recognition plays a significant role in the counterion-induced processibility, morphological features, and physical properties of doped polyaniline (PANI). The interaction of the counterion and solvent controls the chain conformation and, as a result, the formation of extended and localized electronic states; hence, it holds the key for tuning a wide range of electrical and optical properties of doped PANI. The combined effects of counterion, solvent, and processing conditions tune the metal-insulator transition, temperature dependence of conductivity, magnetoresistance, and so forth in doped PANI. The typical examples are shown in the case of PANI doped by camphor sulfonic acid, 2-acrylamido-2-methyl-1-propane sulfonic acid, and dodecylbenzoyl sulfonic acid.     

The molecular potential energy surface and vibrational energy levels of methyl fluoride. Part II

New analytical bending and stretching, ground electronic state, potential energy surfaces for CH(3)F are reported. The surfaces are expressed in bond-length, bond-angle internal coordinates. The four-dimensional stretching surface is an accurate, least squares fit to over 2000 symmetrically unique ab initio points calculated at the CCSD(T) level. Similarly, the five-dimensional bending surface is a fit to over 1200 symmetrically unique ab initio points. This is an important first stage towards a full nine-dimensional potential energy surface for the prototype CH(3)F molecule. Using these surfaces, highly excited stretching and (separately) bending vibrational energy levels of CH(3)F are calculated variationally using a finite basis representation method. The method uses the exact vibrational kinetic energy operator derived for XY(3)Z systems by Manson and Law (preceding paper, Part I, Phys. Chem. Chem. Phys., 2006, 8, DOI: 10.1039/b603106d). We use the full C(3v) symmetry and the computer codes are designed to use an arbitrary potential energy function. Ultimately, these results will be used to design a compact basis for fully coupled stretch-bend calculations of the vibrational energy levels of the CH(3)F system.     

The effect of vibrational energy on the reaction of molecular hydrogen with atomic oxygen

An upper bound of 6 × 10¹⁰ cm³/moles on the rate constant for the reaction of atomic oxygen with vibrationally excited H₂ has been deduced from laboratory observations and from detailed computer calculations. From this result it can be shown that no more than 30% of the vibrational energy of H₂ is effective in overcoming the activation energy for the O + H₂ reaction.