Femtosecond Time-resolved Transient Absorption Spectroscopy Research Articles

Intramolecular electron transfer reactions in meso-(4-nitrophenyl)-substituted subporphyrins.

A2B-type meso-(4-nitrophenyl)-substituted subporphyrins have been synthesized and shown to undergo very fast photoinduced intramolecular charge separation (CS) and charge recombination (CR) between the subporphyrin core and the meso-4-nitrophenyl group in CH2Cl2 as probed by femtosecond time-resolved transient absorption spectroscopy. Red-shifted emissions were detected from charge-separated states as a rare case for porphyrinoids.

Dynamics of Energy and Electron Transfer in the FMO-Reaction Center Core Complex from the Phototrophic Green Sulfur Bacterium Chlorobaculum tepidum

The reaction center core (RCC) complex and the RCC with associated Fenna-Matthews-Olson protein (FMO-RCC) complex from the green sulfur bacterium Chlorobaculum tepidum were studied comparatively by steady-state and time-resolved fluorescence (TRF) and femtosecond time-resolved transient absorption (TA) spectroscopies. The energy transfer efficiency from the FMO to the RCC complex was calculated to be ∼40% based on the steady-state fluorescence. TRF showed that most of the FMO complexes (66%), regardless of the fact that they were physically attached to the RCC, were not able to transfer excitation energy to the reaction center. The TA spectra of the RCC complex showed a 30-38 ps lifetime component regardless of the excitation wavelengths, which is attributed to charge separation. Excitonic equilibration was shown in TA spectra of the RCC complex when excited into the BChl a Qx band at 590 nm and the Chl a Qy band at 670 nm, while excitation at 840 nm directly populated the low-energy excited state and equilibration within the excitonic BChl a manifold was not observed. The TA spectra for the FMO-RCC complex excited into the BChl a Qx band could be interpreted by a combination of the excited FMO protein and RCC complex. The FMO-RCC complex showed an additional fast kinetic component compared with the FMO protein and the RCC complex, which may be due to FMO-to-RCC energy transfer.

The influence of surface passivation on electronic energy relaxation dynamics of CdSe and CdSe/CdS nanocrystals studied using visible and near infrared transient absorption spectroscopy.

Charge carrier relaxation dynamics of electronically excited CdSe and CdSe/CdS core/shell nanocrystals (NCs) were studied using femtosecond time-resolved transient absorption spectroscopy, employing both visible and near-infrared (NIR) probe laser pulses. Following 400 nm excitation, the combination of visible and NIR laser probe pulses were used to determine the influence of surface passivation on electronic relaxation dynamics for nanocrystals overcoated with either organic ligands or inorganic semiconductors. In particular, low-energy NIR photons were used to isolate transient absorption signals due to either electron and hole intraband transitions. Four relaxation components were detected for CdSe NCs passivated by organic molecules: (1) picosecond hole relaxation; (2) electron deep trapping; (3) electron surface trapping; and (4) exciton radiative recombination. Based on TA data collected over a broad energy range, electron deep trapping at Se(2-) sites was suppressed for CdSe NCs passivated by inorganic (CdS) semiconducting materials. By comparing the time-dependent transient absorption data of a series of CdSe/CdS NCs with different shell thicknesses, evidence for the transition from Type-I to quasi Type-II NCs was obtained. These data illustrate the sensitivity of femtosecond time-resolved transient absorption measurements carried out over visible and near infrared probe energies for determining the influence of nanocrystal structure on electronic relaxation dynamics.

Wirelike charge transport dynamics for DNA-lipid complexes in chloroform.

The dynamics of charge separation and charge recombination have been determined for lipid complexes of DNA capped hairpins possessing stilbene electron-acceptor and -donor chromophores separated by base-pair domains that vary in length and base sequence in chloroform solution by means of femtosecond time-resolved transient absorption spectroscopy. The results obtained for the DNA-lipid complexes are compared with those previously obtained in our laboratories for the same hairpins in aqueous buffer. The charge separation and charge recombination times for the lipid complexes are consistently much shorter than those determined in aqueous solution and are only weakly dependent on the number of base pairs separating the acceptor and donor. The enhanced rate constants for forward and return charge transport in DNA-lipid complexes support proposals that solvent gating is responsible, to a significant extent, for the relatively low rates of charge transport for DNA in water. Moreover, they suggest that DNA-lipid complexes may prove useful in the development of DNA-based molecular electronic devices.

BODIPY triads triplet photosensitizers enhanced with intramolecular resonance energy transfer (RET): broadband visible light absorption and application in photooxidation

Resonance energy transfer (RET) was used to enhance the light absorption in triad triplet photosensitizers to access strong and broadband absorption in visible region (from 450–750 nm). This strategy was demonstrated by preparation of (BODIPY)2-diiodo-aza-BODIPY triad (B-2) and (carbazole-styryl BODIPY)2-diiodo-aza-BODIPY triad (B-3), in which the energy donor (BODIPY or styryl-BODIPY) and the energy acceptor (aza-BODIPY, also as the spin converter) parts were connected by click chemistry. Both the energy donors and the energy acceptors show strong absorption in the visible spectral region, but at different wavelengths, therefore the triads show broadband absorption in visible spectra region, e.g. the two major absorption bands of B-3 are located at 593 nm and 683 nm, with e up to 220000 M−1 cm−1 and 81000 M−1 cm−1, respectively. For comparison, a reference compound with only diiodo-aza-BODIPY as the light-harvesting unit was prepared (B-1), which shows only one major absorption band in visible spectral region. Fluorescence studies indicated intramolecular energy transfer for these BODIPY hybrids, a conclusion which is supported by the femtosecond time-resolved transient absorption spectroscopy. Nanosecond transient absorption spectra show that triplet excited states of the dyad and the triad are localized on the iodo-aza-BODIPY part. The compounds were used as triplet photosensitizers for singlet oxygen (1O2) mediated photooxidation of 1,5-dihydroxylnaphthalene and the photosensitizing ability of the new triplet photosensitizers are more efficient than the mono-chromophore based triplet photosensitizers. The molecular design rationale of these RET-enhanced multi-chromophore triplet photosensitizer is useful for development of efficient triplet photosensitizers and for their applications in photocatalysis, photodynamic therapy, photovoltaics and upconversion.

Photoinduced intermolecular electron transfer and off-resonance Raman characteristics of Rhodamine 101/N,N-diethylaniline

The ultrafast photoinduced intermolecular electron transfer (PIET) reaction of Rhodamine 101 (Rh101+) in N,N-diethylaniline (DEA) was investigated using off-resonance Raman, femtosecond time-resolved multiplex transient grating (TG) and transient absorption (TA) spectroscopies. The Raman spectra indicate that the CC stretching vibration of the chromophore aromatic ring is more sensitive to ET compared with the CC stretching mode. The ultrafast photoinduced intermolecular forward ET (FET) from DEA to Rh101+∗ occurs on a time scale of τFET=425–560fs. The backward ET (BET) occurs in the inverted region with a time constant of τBET=46.16–51.40ps. The intramolecular vibrational relaxation (IVR) process occurs on the excited state potential energy surface with the time constant of τIVR=2.77–5.39ps.

Optical Properties and Electronic Energy Relaxation of Metallic Au144(SR)60 Nanoclusters

Electronic energy relaxation of Au144(SR)60(q) ligand-protected nanoclusters, where SR = SC6H13 and q = -1, 0, +1, and +2, was examined using femtosecond time-resolved transient absorption spectroscopy. The observed differential transient spectra contained three distinct components: (1) transient bleaches at 525 and 600 nm, (2) broad visible excited-state absorption (ESA), and (3) stimulated emission (SE) at 670 nm. The bleach recovery kinetics depended upon the excitation pulse energy and were thus attributed to electron-phonon coupling typical of metallic nanostructures. The prominent bleach at 525 nm was assigned to a core-localized plasmon resonance (CLPR). ESA decay kinetics were oxidation-state dependent and could be described using a metal-sphere charging model. The dynamics, emission energy, and intensity of the SE peak exhibited dielectric-dependent responses indicative of Superatom charge transfer states. On the basis of these data, the Au144(SR)60 system is the smallest-known nanocluster to exhibit quantifiable electron dynamics and optical properties characteristic of metals.

Photoinduced electron transfer of Rhodamine 6G/N,N-diethylaniline revealed by multiplex transient grating and transient absorption spectroscopies

The dynamics and spectroscopic characteristics of the ultrafast photoinduced electron transfer (ET) of Rhodamine 6G (Rh6G+) in N,N-diethylaniline (DEA) were studied using femtosecond time-resolved multiplex transient grating and transient absorption spectroscopies. The ultrafast photoinduced forward ET from DEA to the Rh6G+* cation radical excited state has a time constant of τFET = 219–318 fs. The much slower backward ET from the neutral radical Rh6G· to DEA+ with a time constant of τBET = 22.76–42.31 ps occurs in the inverted region. Intramolecular vibrational relaxation of the excited state takes place in τIVR = 2.18–6.91 ps.

Ultrafast electronic deactivation dynamics of the inosine dimer — a model case for H-bonded purine bases

The structural properties and ultrafast electronic deactivation dynamics of the inosine dimer in CHCl3 have been investigated by two-dimensional (1)H NMR and static FTIR spectroscopy and by femtosecond time-resolved transient absorption spectroscopy, respectively. The (1)H NMR and IR spectra show the formation of a well-defined, symmetric dimer with an association equilibrium constant of KI·I = 690 ± 100 M(-1). The excited-state dynamics after photoexcitation at λpump = 260 nm monitored by ultrafast absorption spectroscopy show great similarity with those of the monomer inosine in an aqueous solution and are governed by a decay time of τ = 90 ± 10 fs, which is one of the shortest electronic lifetimes of all nucleobases and nucleobase dimers studied so far. On the basis of these observations, the inosine dimer is expected to follow a similar relaxation pathway as the monomer, involving an out-of-plane deformation of the six-membered ring. The importance of the C(2) position for the electronic deactivation of hypoxanthine and guanine is discussed. The obtained well-determined structure and straightforward dynamics qualify the inosine dimer as an excellent reference case for more complicated systems such as the G·G dimer and the G·C and A·T Watson-Crick pairs.

Remarkable Enhancement of Photocatalytic Hydrogen Evolution Efficiency Utilizing An Internal Cavity of Supramolecular Porphyrin Hexagonal Nanocylinders Under Visible-Light Irradiation

An efficient visible light-induced hydrogen evolution system has been developed by using supramolecular porphyrin hexagonal nanocylinders that encapsulate Pt-colloids-deposited TiO2 nanoparticles (Pt/TiO2) in the internal cavity. First, porphyrin nanocylinders structurally controlled by encapsulated Pt/TiO2 are prepared via a solvent mixture technique. The bar-shaped structure composed of Pt/TiO2 and zinc meso-tetra(4-pyridyl)porphyrin [ZnP(Py)4] is formed with the aid of a surfactant: cetyltrimethylammonium bromide (CTAB) in a DMF/H2O mixture solution [denoted as Pt/TiO2–ZnP(Py)4 nanorods]. In scanning electron microscopy (SEM) measurements, ZnP(Py)4 pristine hexagonal nanocylinder with a large hollow structure [denoted as ZnP(Py)4 nanocylinder] was observed, whereas the hollow hole was completely closed in case of Pt/TiO2–ZnP(Py)4 nanorods. X-ray diffraction (XRD) analyses also revealed that ZnP(Py)4 alignment in the nanorod was based on the stacked-assemblies of ZnP(Py)4 coordinated hexagonal formations. These results clearly indicate that Pt colloids-deposited TiO2 nanoparticles (Pt/TiO2) were successfully encapsulated within a ZnP(Py)4 hexagonal nanocylinder. Pt/TiO2–ZnP(Py)4 also shows a broadened absorption in the visible region because of aggregation of ZnP(Py)4. Then, Pt/TiO2–ZnP(Py)4 exhibited efficient hydrogen evolution under visible light irradiation, whereas no hydrogen was evolved in the case of Pt/TiO2 without ZnP(Py)4. In addition, the hydrogen evolution efficiency of Pt/TiO2–ZnP(Py)4 nanorods per unit weight of Pt was two orders magnitude greater than that of the nonencapsulated system: Pt/TiO2 and ZnP(Py)4 nanocylinder composites [Pt/TiO2 + ZnP(Py)4 composites]. Finally, the photodynamics of the excited state of Pt/TiO2–ZnP(Py)4 nanorods was examined by femtosecond time-resolved transient absorption spectroscopy to clarify the photocatalytic mechanism.

Spectroscopic properties of the Chlorophyll a–Chlorophyll c 2–Peridinin-Protein-Complex (acpPC) from the coral symbiotic dinoflagellate Symbiodinium

Femtosecond time-resolved transient absorption spectroscopy was performed on the chlorophyll a-chlorophyll c 2-peridinin-protein-complex (acpPC), a major light-harvesting complex of the coral symbiotic dinoflagellate Symbiodinium. The measurements were carried out on the protein as well on the isolated pigments in the visible and the near-infrared region at 77 K. The data were globally fit to establish inter-pigment energy transfer paths within the scaffold of the complex. In addition, microsecond flash photolysis analysis was applied to reveal photoprotective capabilities of carotenoids (peridinin and diadinoxanthin) in the complex, especially the ability to quench chlorophyll a triplet states. The results demonstrate that the majority of carotenoids and other accessory light absorbers such as chlorophyll c 2 are very well suited to support chlorophyll a in light harvesting. However, their performance in photoprotection in the acpPC is questionable. This is unusual among carotenoid-containing light-harvesting proteins and may explain the low resistance of the acpPC complex against photoinduced damage under even moderate light conditions.

Charge transfer relaxation in donor–acceptor type conjugated materials

The development of conjugated materials bearing electron-rich and electron-poor units along their backbone introduces new possibilities to control functionality for organic electronic applications through charge transfer character in ground and excited states. A thorough understanding of intramolecular dipoles and their evolution during excited state relaxation is necessary in order to fully exploit this opportunity. PCDTBT is an alternating donor–acceptor copolymer with high photovoltaic efficiency in bulk heterojunction solar cells. We use time-resolved femtosecond transient absorption spectroscopy in solution and in the solid state to study PCDTBT and the dTBT and CDTBT model compounds, fragments of the polymer chain. Higher solubility and slower relaxation make CDTBT particularly suitable to understand the mechanism of charge transfer relaxation in this class of materials. A progressive increase of charge transfer character from the initially moderately polar excited state is mainly driven by solvent reorganization and some torsional rearrangements. Similar relaxation in solid state CDTBT might ultimately lead to the formation of separate charges.

Excitation Energy Transfer in Isolated Chlorosomes from Chlorobaculum tepidum and Prosthecochloris aestuarii

Excitation energy transfer in chlorosomes from photosynthetic green sulfur bacteria, Chlorobaculum (Cba.) tepidum and Prosthecochloris (Pst.) aestuarii, have been studied at room temperature by time-resolved femtosecond transient absorption spectroscopy. Bleach rise times from 117 to 270 fs resolved for both chlorosomes reflect extremely efficient intrachlorosomal energy transfer. Bleach relaxation times, from 1 to 3 ps and 25 to 35 ps, probed at 758 nm were tentatively assigned to intrachlorosomal energy transfer based on amplitude changes of the global fits and model calculations. The anisotropy decay constant of about 1 ps resolved at 807 nm probe wavelength for the chlorosomes from Chloroflexus aurantiacus, Pst. aestuarii and Cba. tepidum was related to energy transfer between bacteriochlorophyll a molecules of the baseplate and partly to intrachlorosomal energy transfer. The longer anisotropy components 6.6, 8.8 and 12.1 ps resolved for the three chlorosomes, respectively, were assigned to chlorosome to baseplate energy transfer. Global fits of magic-angle data also revealed longer chlorosome to baseplate energy transfer components from 95 to 135 ps, in accord with results from simulations.

Relaxation dynamics of Au25L18 nanoclusters studied by femtosecond time-resolved near infrared transient absorption spectroscopy

The relaxation dynamics of electronically excited [Au(25)(SR)(18)](q), where q = 0 or -1 and SR = S(CH(2))(2)Ph, were studied using femtosecond time-resolved transient absorption spectroscopy. Nanoclusters excited by 400 nm light were probed using temporally delayed broad-bandwidth continuum probe pulses. Continuum pulses were generated in both the visible and near infrared (NIR) spectral regions, providing access to a wide range of transient spectral features. The use of NIR probe pulses allowed the relaxation dynamics of the excited states located near the HOMO-LUMO energy gap to be monitored in the probe step via the sp ← LUMO and sp ← LUMO+1 transitions. These NIR measurements yielded excited state absorption (ESA) data that were much less congested than the typical visible transient spectrum. For the neutral nanocluster, the time-domain data were composed of three components: (1) a few-picosecond decay, (2) a slower decay taking a few hundred picoseconds and (3) a non-decaying plateau function. Component 1 reflected energy relaxation to semi-ring ligand states; component 2 was attributed to relaxation via a manifold of states located near the HOMO-LUMO energy gap. Component 3 arose from slow radiative recombination. The dynamics of the anion depended upon the identity of the excited state from which the particle was relaxing. The LUMO+1 state of the anion exhibited relaxation dynamics that were similar to those observed for the neutral nanocluster. By comparison, the time-domain data observed for the LUMO state contained only two components: (1) a 3.3 ± 0.2 ps decay and (2) a 5 ± 1 ns decay. The amplitude coefficients of each component were also analyzed. Taken together, the amplitude coefficients and lifetimes were indicative of an activation barrier located approximately 100 meV above the HOMO-LUMO energy gap, which mediated a previously unobserved excited state decay process for [Au(25)(SR)(18)](0). These data suggested that NIR ESA measurements will be instrumental in describing the relaxation processes of quantum-confined nanoclusters.

Ultrafast charge-transfer dynamics of donor-substituted truxenones

The photophysics of two donor-substituted truxenone derivatives has been studied by femtosecond time-resolved transient absorption spectroscopy. The systems consist of a central truxenone acceptor with three triarylamine (TARA) branches which act as electron donors. Upon excitation in the visible regime an electron is transferred from the donor to the acceptor, generating a charge-separated state. This state can be probed via the characteristic absorption of the TARA radical cation around 700 nm. A second absorption band around 420 nm exhibits the same kinetics and is assigned to an absorption of the radical anion of the truxenone moiety. The back electron transfer and the recovery of the ground state can be interpreted within the framework of Marcus theory. To study the dependence of the back electron transfer on the electronic coupling, the distance between the donor and the acceptor was adjusted. Two solvents were employed, dimethylsulfoxide and dichloroethane. A biexponential decay of the bands assigned to the charge-separated state was observed, with time constants in the picosecond range. Surprisingly, the rates for electron back transfer do not follow the simple picture of the donor-acceptor distance being the determining factor. The observations are explained within a model that additionally takes steric interactions between the donor and the acceptor into account.

Ultrafast time-resolved spectroscopy of the light-harvesting complex 2 (LH2) from the photosynthetic bacterium Thermochromatium tepidum

The light-harvesting complex 2 from the thermophilic purple bacterium Thermochromatium tepidum was purified and studied by steady-state absorption and fluorescence, sub-nanosecond-time-resolved fluorescence and femtosecond time-resolved transient absorption spectroscopy. The measurements were performed at room temperature and at 10 K. The combination of both ultrafast and steady-state optical spectroscopy methods at ambient and cryogenic temperatures allowed the detailed study of carotenoid (Car)-to-bacteriochlorophyll (BChl) as well BChl-to-BChl excitation energy transfer in the complex. The studies show that the dominant Cars rhodopin (N=11) and spirilloxanthin (N=13) do not play a significant role as supportive energy donors for BChl a. This is related with their photophysical properties regulated by long π-electron conjugation. On the other hand, such properties favor some of the Cars, particularly spirilloxanthin (N=13) to play the role of the direct quencher of the excited singlet state of BChl.

Direct Observation of Temperature-Dependent Excited-State Equilibrium in Dinuclear Ruthenium Terpyridine Complexes Bearing Electron-Poor Bridging Ligands

Dinuclear ruthenium–terpyridine complexes, bearing highly conjugated bridging ligands, have been investigated by time- and temperature-dependent emission spectroscopy, femtosecond time-resolved transient-absorption spectroscopy, and time-dependent density functional theory calculations. These terpyridine compounds show room-temperature emission around 640 nm and lifetimes between 140 and 230 ns. Reduction of the temperature results in an overall increase of emission lifetime. However, the specific temperature dependence of the luminescence lifetime depends on the particular bridging ligand. This ligand-specific behavior is found to correlate with the electronic structure of the ligand, which indicates an excited-state equilibrium between a highly delocalized 3MLCT and a ligand-centered 3ππ* excited-state. Due to this equilibrium a prolonged room-temperature lifetime is observed.

Photochemistry of 2-Naphthoyl Azide. An Ultrafast Time-Resolved UV–Vis and IR Spectroscopic and Computational Study

The photochemistry of 2-naphthoyl azide was studied in various solvents by femtosecond time-resolved transient absorption spectroscopy with IR and UV-vis detection. The experimental findings were interpreted with the aid of computational studies. Using polar and nonpolar solvents, the formation and decay of the first singlet excited state (S(1)) was observed by both time-resolved techniques. Three processes are involved in the decay of the S(1) excited state of 2-naphthoyl azide: intersystem crossing, singlet nitrene formation, and isocyanate formation. The lifetime of the S(1) state decreases significantly as the solvent polarity increases. In all solvents studied, isocyanate formation correlates with the decay of the azide S(1) state. Nitrene formation correlates with the decay of the relaxed S(1) state only upon 350 nm excitation (S(0) → S(1) excitation). When S(n) (n ≥ 2) states are populated upon excitation (λ(ex) = 270 nm), most nitrene formation takes place within a few picoseconds through the hot S(1) and higher singlet excited states (S(n)) of 2-naphthoyl azide. The data correlate with the results of electron density difference calculations that predict nitrene formation from the higher-energy singlet excited states, in addition to the S(1) state. For all of these experiments, no recovery of the ground state was observed up to 3 ns after photolysis, which indicates that both internal conversion and fluorescence have very low efficiencies.

Exciton‐Coupled Charge‐Transfer Dynamics in a Porphyrin J‐Aggregate/TiO2 Complex

Exciton-coupled charge-transfer (CT) dynamics in TiO(2) nanoparticles (NP) sensitized with porphyrin J-aggregates has been studied by femtosecond time-resolved transient absorption spectroscopy. J-aggregates of 5,10,15-triphenyl-20-(3,4-dihydroxyphenyl) porphyrin (TPPcat) form CT complexes on TiO(2) NP surfaces. Catechol-mediated strong CT coupling between J-aggregate and TiO(2) NP facilitates interfacial exciton dissociation for electron injection into the conduction band of the TiO(2) nanoparticle in pulse width limited time (<80 fs). Here, the electron-transfer (<80 fs) process dominates over the intrinsic exciton-relaxation process (J-aggregates: ca. 200 fs) on account of exciton-coupled CT interaction. The parent hole on J-aggregates is delocalized through J-aggregate excitonic coherence. As a result, holes immobilized on J-aggregates are spatially less accessible to electrons injected into TiO(2) , and thus the back electron transfer (BET) process is slower than that of the monomer/TiO(2) system. The J-aggregate/porphyrin system shows exciton spectral and temporal properties for better charge separation in strongly coupled composite systems.

Photodissociation of thioglycolic acid studied by femtosecond time-resolved transient absorption spectroscopy

Steady-state and time-resolved spectroscopies were employed to study the photodissociation of both the neutral (HS-CH(2)-COOH) and doubly deprotonated ((-)S-CH(2)-COO(-)) forms of thioglycolic acid (TGA), a common surface-passivating ligand used in the aqueous synthesis and organization of semiconducting nanostructures. Room temperature UV-Vis absorption spectroscopy indicated strong absorption by the S(1) and S(2) excited states at 250 nm and 185 nm, respectively. The spectrum also contained a weaker absorption band that extended to approximately 550 nm, which was assigned to the π(CO) (*)←n(O) transition. Femtosecond time-resolved transient absorption spectroscopy was performed on TGA using 400 nm excitation and a white-light continuum probe to provide the temporally and spectrally resolved data. Both forms of TGA underwent a photoinduced dissociation from the excited state to form an α-thiol-substituted acyl radical (α-TAR, S-CH(2)-CO(●)). For the acidic form of TGA, radical formation occurred with an apparent time constant of 60 ± 5 fs; subsequent unimolecular decay took 400 ± 60 fs. Similar kinetics were observed for the deprotonated form of TGA (70 ± 10 fs radical formation; 420 ± 40 fs decay). The production of the α-TAR was corroborated by the observation of its characteristic optical absorption. Time-resolved data indicated that the photoinduced dissociation of TGA via cleavage of the C-OH bond occurred rapidly (≤100 fs). The prevalence of TGA in aqueous semiconducting nanoparticles makes its absorption in the visible spectral region and subsequent dissociation key to understanding the behavior of nanoscale systems.