Chemical Physics Letters (v.416, #1-3)

Dye-sensitized solar cells using retinoic acid and carotenoic acids: Dependence of performance on the conjugation length and the dye concentration by Xiao-Feng Wang; Ritsuko Fujii; Seigo Ito; Yasushi Koyama; Yumiko Yamano; Masayoshi Ito; Takayuki Kitamura; Shozo Yanagida (1-6).
Titanium oxide-based dye-sensitized solar cells (DSSC) were fabricated by the use of retinoic acid and carotenoic acids having the number of conjugated double bonds, n  = 5–13. The incident photon-to-current conversion efficiency, the photocurrent density and the solar energy-to-electricity conversion efficiency exhibited the highest values at n  = 7, and then decreased toward both sides. The effects of dilution of CA7 with deoxycholic acid were also examined. The above parameters per unit CA7 concentration progressively increased toward the lowest concentration, which is ascribed to the isolated excitation free from singlet–triplet annihilation in the dye molecules on the TiO2 layer.

First-principles comparative study of the pressure-induced phase transition of NaSbO3 and NaBiO3 by Xiao-Juan Liu; Zhi-Jian Wu; Xian-Feng Hao; Hong-Ping Xiang; Jian Meng (7-13).
The phase transformations of NaSbO3 and NaBiO3 from ilmenite phase to the orthorhombic phase are predicted within the density functional theory (DFT) using the generalized gradient approximation. The bonding properties of the covalent band maximum and the conduction band bottom are used to elucidate the comparatively large band gap in the ilmenite phase to the orthorhombic phase. Bond populations and atomic electronnegativities are used to explain the comparatively small energy gap of NaBiO3 to NaSbO3. The abnormal phenomenon that the band gap increases with the increasing of hydrostatic pressure is explained to be more distorting during the pressure increase.

Dissociation energies and ionization potentials of neutral and singly-charged fullerenes have been obtained from density functional theory calculations for sizes ranging from 40 to 70 atoms. Good agreement with available experimental data has been obtained. Our results confirm that magic number fullerenes with n  = 50, 60 and 70 present the largest ionization potentials and dissociation energies. We have found that the most stable isomer for n  = 62 is a non-classical structure with a chain of four adjacent pentagons surrounding a heptagon, and for n  = 50 is a structure of D3 symmetry that violates the pentagon adjacency penalty rule. Both unusual structures lead to the best agreement with experiment.

High-pressure synthesis of carbon nanotubes with a variety of morphologies by Hui Yang; Philippe Mercier; Shiunchin C. Wang; Daniel L. Akins (18-21).
Facile synthesis of carbon nanotubes in large quantity can be accomplished by direct thermal decomposition of ethanol in a stainless steel reaction chamber under high pressure. Raman and thermogravimetric data indicate that the as-synthesized carbon nanotubes are of high quality, with the prepared samples exhibiting low amorphous carbon content. TEM measurements confirm the formation of carbon nanotubes of several morphologies for the high-pressure synthesis. At pressures near atmospheric, however, very limited morphologies and yields for the nanotubes result. A mechanism involving catalytic site formation as a result of temperature dependent surface roughening is consistent with our observations.

A diode pumped Vertical Cavity Surface Emitting Laser emitting at 2.3 μm has been developed to extend the near infrared spectral region accessible for Intracavity Laser Absorption Spectroscopy. The achieved sensitivity on the order of α min  ∼ 1.5 × 10−9  cm−1 (or 3 × 10−10  cm−1/ Hz ), has allowed detecting water and carbon dioxide lines with an intensity as low as 10−27 and 2 × 10−28  cm/molecule, respectively. The first detection of the 31104-00001 band of 13C16O2 and of a number of transitions of the 31104-00001 and 40005-01101e bands of 12C16O2 is reported together with their rotational analysis.

A multi-temperature X-ray diffraction study was performed on the colossal magnetoresistive thiospinel FeCr2S4 to find out if structural phase transitions are associated with the magnetic transitions of the two Fe and Cr sublattices. The temperature dependence of the cell parameters was carefully screened, and the crystal structure was determined at four different temperatures. The present X-ray diffraction experiment, the first performed on a single crystal, confirms that bulk FeCr2S4 is not subject to structural phase transformations in the temperature range 293–23 K. The occurrence of the forbidden (0 0 2) reflection and the non-stoichiometric sample composition are discussed.

A noisy biological system is applied to investigate the influence of coupling on the internal stochastic resonance. It is found that the internal stochastic resonance could be transferred by coupling, and the enhancement and suppression of the stochastic resonance could be realized by controlling the coupling strength at proper range. The explicit internal signal stochastic resonance without tuning occurs. An appropriate coupling strength is found to enhance the propagation of the internal stochastic resonance most effectively with the increment of the external noise.

Pair-wise resonance in catacondensed hexagonal systems by Khaled Salem; Maolin Zheng; Ivan Gutman (38-41).
In catacondensed hexagonal systems, a set of pair-wise resonant hexagons is resonant [Croat. Chem. Acta 56 (1983) 365], [J. Mol. Struct. (Theochem) 279 (1993) 41]. The first proof of this result was given by Hansen and Zheng [J. Mol. Struct. (Theochem) 279 (1993) 41]. Here we offer an alternative proof.

Small-molecule organic solar cells with improved stability by Q.L. Song; F.Y. Li; H. Yang; H.R. Wu; X.Z. Wang; W. Zhou; J.M. Zhao; X.M. Ding; C.H. Huang; X.Y. Hou (42-46).
A stable small-molecule organic photovoltaic device with structure of ITO⧹donor⧹acceptor⧹buffer⧹cathode is presented. A thin layer (∼60 Å) of tris-8-hydroxy-quinolinato aluminum (Alq3) instead of bathocuproine (BCP) is adopted as the buffer of the device, resulting in 150 times longer lifetime. The power conversion efficiency of the device is 2.11% under 75 mW/cm2 AM1.5G simulated illumination, and no perceptible efficiency degradation is observed for long-term storage of the device in vacuum or nitrogen-filled glove box. More effective blocking of Alq3 than BCP against diffusion of cathode atoms and permeation of oxygen and/or water molecules is considered as the main reason for the improved performance of the new device.

Deuterium NMR spectral patterns observed at 61.4 MHz in a magneto-aligned ferroelectric phase of a partially deuterated smectogen are quantitatively interpreted based on Landau theory to understand the soliton-like distortion of the helicoidal structure. The distortion is induced gradually by rotating the sample in the NMR magnet using a goniometer probe. At each temperature, the simulation of angular dependent spectra enables us to determine the critical field for unwinding the helix. The study maps out a part of the (H, T) phase diagram.

The reactivity and behavior of phenol (phenol-d 5) on NaX zeolite at different temperatures have been studied by 1H MAS NMR and FT-IR techniques. An interaction between hydroxyl of phenol and zeolite framework oxygen atoms has been revealed, favouring the transfer of H(D) atoms of phenolic hydroxyl to zeolite framework to give phenolate ions. In phenol, the isotope exchange between H(D) atoms of phenolic hydroxyl and those of ring occurs mainly at ortho and para positions. The formation of phenolate ions changes the isotope exchange to meta position. The formation of phenol to phenolate ions is enhanced on NaX zeolite, explaining the high O-alkylation selectivity observed in phenol alkylation with methanol.

Spin–orbit relativistic time dependent density functional theory calculations for the description of core electron excitations: TiCl4 case study by G. Fronzoni; M. Stener; P. Decleva; F. Wang; T. Ziegler; E. van Lenthe; E.J. Baerends (56-63).
The recent time-dependent density functional theory approach within the two-component zero order relativistic approximation implemented in the ADF code has been modified in order to treat core electron excitations. The method has been applied to the calculation of the Ti 2p (L2,3) core excitation spectrum in the TiCl4 molecule. The results obtained allow to correctly describe both the L3 and L2 manifold of Ti 2p core excited states. Different XC potential have been used in the calculations showing that the results are not very sensitive to the exchange correlation potential choice, provided the asymptotic behaviour is correct.

Observation of a substantially-bound excited-core Rydberg state in I2 by optical triple resonance by A. Marica Sjödin; Trevor Ridley; Kenneth P. Lawley; Robert J. Donovan (64-69).
A substantially-bound (D e  ∼ 7000 cm−1, R e  ∼ 3.1 Å, T e  ∼ 60 546 cm−1) 6s Rydberg state of I2 with 0 u + symmetry based on the lowest excited state of the ion core, previously labelled a ( 4 Σ u , 1 / 2 - ) , has been identified using optical triple resonance via the B ( 0 u + ) and E 0 g + ( 3 P 2 ) states together with resonance ionization. The interactions with ground-core Rydberg states that the new state undergoes and the reasons why it is observed in the resonance ionization spectrum via the E 0 g + ( 3 P 2 ) state, whilst the A [ 2 Π u , 1 / 2 ] c ; 6 s 0 u + state is not, are explained in terms of its electronic configuration.

We report a study of the inclusion complex of p-chlorophenol inside α-cyclodextrin (α-CD) by the theory of atoms in molecules (AIM). We use a quantitative comparison of some AIM properties of isolated p-chlorophenol (PCP) and the inclusion complex (PCP-CD) and we characterize some weak interactions within the host–guest complex. Furthermore, we compare the electrophilic aromatic substitution on the p-chlorophenol in the isolated state and inside α-CD. The analysis of the bond critical points of PCP shows that there is no trend in the effect on the AIM properties of PCP due to inclusion in the α-CD.

Ultraviolet photodetectors with low temperature synthesized vertical ZnO nanowires by Cheng-Liang Hsu; Shoou-Jinn Chang; Yan-Ru Lin; Pin-Chou Li; Tzer-Shen Lin; Song-Yeu Tsai; Tsung-Heng Lu; I-Cherng Chen (75-78).
Vertical single-crystal ZnO nanowires of were grown on ZnO:Ga/glass template by self-catalyzed vapor–liquid–solid (VLS) process at a low temperature of 520 °C. It was found that length of these ZnO nanowires was around 2.0 μm while the diameter of these nanowires was in between 70 and 150 nm. It was also found that the ZnO nanowires were structurally uniform, defect free and well oriented with pure wurtzite structure. UV photodetectors were then fabricated using a simple scheme. It was found that photocurrent to dark current contrast ratio of our ZnO nanowires photodetector was 67.5.

The present Letter reports electrical and optical properties of our newly synthesized organic-titanium hybrid polymer, (2,3-dicyanophenyl bis-2,4-pentanedionate titanium alkoxide) (PDC–PD–Ti). The main chains of PDC–PD–Ti consist of alternate titanium ions and phenylene groups by way of oxygen atoms. Electrically poled amorphous polymer systems are active in pyroelectricity, because of ordering of the cyanate groups in the side chains. The linear optical response is likely associated with a photo-excitation into a delocalized electronic excited level extending from titanium ion to π-conjugated phenylene group. Furthermore, the material exhibits second order nonlinear optical activity after the electrical poling procedure.

The photoactivation of the plant photoreceptor phytochrome is governed by a red-light-induced C15-Z  → C15-E isomerization of the tetrapyrrolic chromophore phytochromobilin. From the viewpoint of experimental studies, ambiguity prevails as to whether the photoactivation involves a proton transfer from the chromophore to the surrounding protein. Here, we report a theoretical study addressing the effect of phytochromobilin protonation state on its photoisomerization by means of quantum chemical calculations. It is found that neutral forms of the chromophore are much less likely to photoisomerize than the parent, protonated form – a finding which supports the view that phytochromobilin remains protonated during phytochrome photoactivation.

The excited state reaction of a diphenyl methane dye, auramine O (AO), has been studied in water/AOT/heptane reverse micelles. When compared with bulk aqueous solution the reaction rate is strongly suppressed in the dispersed phase, and the kinetics are non-single exponential. The reaction rate is a strong function of micelle radius, increasing with increasing size. The results are discussed in terms of increased friction along the reactive coordinate due to confinement of the water phase and equilibrium between AO bound at the water/surfactant interface and in the dispersed water phase.

Intramolecular charge transfer in the porphyrin–oligothiophene–fullerene triad by Mengtao Sun; Peng Song; Yuehui Chen; Fencai Ma (94-99).
Intramolecular charge transfer (ICT) in porphyrin–oligothiophene–fullerene triad was reported experimentally [J. Ikemoto, K. Takimiya, Y. Aso. T. Otsubo, M. Fujitsuka, O. Ito, Org. Lett. 4 (2002) 309], and the weak distance dependence of the oligothiophene spacer was found. In this Letter, ICT in this triad is theoretically investigated with quantum chemistry method as well as the 2D and 3D real space analysis methods. The calculated transition energies and oscillator strengths are consistent with the experimental data. The theoretical analysis with 2D and 3D real space analysis reveal that there are two ICT mechanisms. The experimental weak distance dependence of the oligothiophene spacer is benefitted from the superexchange mechanism.

Time-resolved infrared absorption spectra of photoexcited benzophenone (BP) in carbon tetrachloride and benzene were measured with the use of a dispersive nanosecond time-resolved infrared spectrometer. The vibrational infrared spectrum of BP in the n–π* T1 state (T1 BP) was obtained. The CO stretch mode of T1 BP was not observed in contrast to the transient Raman spectra reported previously. In addition, a broad electronic absorption band ascribable to the T2  ← T1 transition was observed in the wavenumber region higher than ∼2000 cm−1. Those results indicate that time-resolved infrared spectroscopy is powerful not only for observing vibrational transitions in an excited electronic state but also for examining transitions among closely lying excited electronic states of conjugated molecular systems.

As shown by Milne in the early days of quantum mechanics, the non-relativistic binding energy of a heavy neutral atom with nuclear charge Ze is proportional to Z 7/3 in the large Z limit. Correction terms of order Z 2 and Z 5/3 to Milne’s limiting large Z result were first calculated by Scott. Here, the question as to the power of Z at which correlation energy first appears in such a binding energy formula is addressed. It is shown that a recent approximation proposed by one of us (ÁN) supports an earlier extrapolation from large dimensionality D to D  = 3 by Herschbach and co-workers, that correlation energy enters the large Z binding energy formula for the first time at o(Z 4/3).

The 12Π(X2Π), 22Π, 12Σ+, 32Π, 42Π, and 22Σ+ states of the OCS+ ion were studied using the CASSCF and CASPT2 methods with a contracted ANO basis and 32Π and 42Π are characterized as shake-up ionization states. The CASSCF frequency calculations indicate that the 12Π, 22Π, 12Σ+, and 22Σ+ primary ionization states represent minima in the potential energy surfaces (PESs), and accurate CASPT2 adiabatic excitation energy (T 0) calculations support assignments of the A, B, and C states to 22Π, 12Σ+, and 22Σ+, respectively. The CASSCF frequency calculations indicate that 32Π and 42Π represent saddle points in the PESs. We found minima in the PESs of the 52A′ and 42A″ states (related to 42Π), and the CASPT2 T 0 values for 52A′ and 42A″ are between the T 0 values of B2Σ+ and C 2Σ+. The observed satellite bands between the B and C bands in spectrum can be (partially) attributed to 52A′ and 42A″.

A benchmark electronic structure study of the Wellington elimination by Jerzy Cioslowski; David Moncrieff (113-115).
High-level electronic structure calculations accurately reproduce activation and reaction energies of dihydrogen eliminations from cyclic C4H6X molecules. In agreement with the original proposal of Wellington, transition states corresponding to a concerted mechanism are found at the CCSD/aug-cc-pVDZ level of theory. The initial distance between the departing hydrogens determines qualitatively the position of the transition state on the reaction path and (to a lesser extent) its energetics. The excellent agreement between the computed and experimental energies makes the present calculations suitable as a benchmark for calibration of lower-level approaches to be employed for larger heterocycles.

A new general approach is developed for obtaining systematic sequences of atomic single-particle basis sets for use in correlated electronic structure calculations of molecules. All the constituent functions are defined as the solutions of variational problems and are of three types: a minimal Hartree–Fock set, additional functions to represent low-lying excited configurations, and general functions for describing electron correlation. The latter are determined to minimize a functional derived from the closed-shell second-order correlation energy expression. Generally-contracted Gaussian expansions are developed to approximate these general functions in the non-relativistic case and within a scalar-relativistic approximation.

The vibrational coherence of the H–Cl oscillator in the monomer as well as in small clusters ((HCl) x and (HCl) x (N2) n ) trapped in argon and nitrogen matrices is explored by means of time-resolved one color degenerate four wave mixing experiments. The time and spectral resolution of the laser source, a picosecond OPO laser, enables the measurement of the vibrational dephasing time of HCl in various well defined (HCl) x (N2) n structures. The results highlight the environment effect on the dephasing processes.

Energy relaxation paths in matrix-isolated excited molecules: Comparison of porphycene with dibenzoporphycenes by Jacek Dobkowski; Yauheni Lobko; Sylwester Gawinkowski; Jacek Waluk (128-132).
When excited with large excess of energy over the lowest excited singlet state, two alkyl derivatives of dibenzo[cde, mno]porphycene undergo rapid relaxation to S1. The S1 depopulation occurs in 10–20 ps, leading directly to S0. The relaxation rates are only weakly temperature or medium-dependent. This behavior contrasts with properties of parent porphycene, where the relaxation is much slower in argon matrices: after excitation into S3/S4, it takes about 100 ps to reach S1, which then decays in 15 ns. The differences are explained by the planarity and rigidity of parent porphycene, as opposed to nonplanar, flexible structure of dibenzo derivatives.

Optical transition probabilities of Er3+ ions in La2CaB10O19 crystal by Rui Guo; Yicheng Wu; Peizhen Fu; Fangli Jing (133-136).
Optical absorption and emission intensity have been investigated for a new erbium-doped lanthanum calcium borate crystal Er3+:La2CaB10O19 (Er:LCB), and spectral parameters have been estimated from absorption data based on Judd–Ofelt theory. The three intensity parameters Ω t (t  = 2, 4, 6) are 3.50 × 10−20, 4.02 × 10−20 and 1.64 × 10−20  cm2, respectively. From the obtained intensity parameters, the radiative probabilities A r, radiative lifetime τ f, fluorescence branching ratios β c and integrated emission cross-sections Σ have been calculated. In comparison with other Er-doped laser crystals, the results show that Er:LCB has potential as a promising laser crystal.

The present work describes how the hydrogen adsorption capacity of graphitic materials in the temperature range between 100 and 300 K can be derived from experimental vibrational energy spectra as well as from results of high level ab initio calculations. It has been found that wrong long-range behavior observed by standard ab initio calculations strongly affects the accuracy of the predicted storage capacity. We have proposed an improved semi-empirical algorithm to calculate adsorption properties. The empirical potential described by Mattera and co-workers in combination with an ab initio calculated parameter set gives a proper theoretical description of the graphite–hydrogen interaction.

In molecular optimal control theory a laser pulse is designed to drive a molecular system to a target value of an observable. To be feasible in the laboratory, the optimal electric field must have a finite amplitude. Current algorithms limit the maximum amplitude indirectly by constraining the field’s energy. We introduce a trigonometric mapping for the field amplitude to limit the maximum amplitude explicitly. In a calculation with hydrogen fluoride we show that an explicit amplitude constraint is particularly important when we account for the electric field’s effect on the electronic structure.

The supersonic beam method combined with techniques of laser spectroscopy has been applied to determine the repulsive wall of the D10+(1Σ+) excited-state potential of CdAr and CdKr molecules. The molecules were produced in a continuous supersonic-expansion beam and excited with a dye-laser beam directly from the X10+(1Σ+) to the excited state. Analysis of the laser-induced fluorescence of the unstructured continuum ← bound profiles, recorded for the first time in excitation at the D10+  ← X10+ transition, yielded information on the short range D10+-state potential of the molecules.

Water VUV electronic state spectroscopy by synchrotron radiation by R. Mota; R. Parafita; A. Giuliani; M.-J. Hubin-Franskin; J.M.C. Lourenço; G. Garcia; S.V. Hoffmann; N.J. Mason; P.A. Ribeiro; M. Raposo; P. Limão-Vieira (152-159).
Electronic state spectroscopy of water has been studied using synchrotron radiation. The spectra presented in this Letter represent the highest resolution (∼0.075 nm) measurements in the energy range 6.0–11.0 eV and have allowed a detailed analysis of several new vibrational progressions to be observed in the 8.5–10 eV region and enabled us to assign the Rydberg series in the 9.9–10.8 eV energy absorption for the first time. Absolute cross-sections are also reported and compared with the previous data.

Dissociation energies, ionization potentials and electron affinities of three perfluoroalkyl iodides, CF3I, C2F5I, and i-C3F7I are calculated accurately with B3LYP, MP n (n  = 2–4), QCISD, QCISD(T), CCSD, and CCSD(T) methods. Calculations are performed by using large-core correlation-consistent pseudopotential basis set (SDB-aug-cc-pVTZ) for iodine atom. In all energy calculations, the zero point vibration energy is corrected. And the basis set superposition error is corrected by counterpoise method in the calculation of dissociation energy. Theoretical results are compared with the experimental values.

A comprehensive analysis of the spectral behaviour of the first UV band for t-stilbene (trans-1,2,diphenylethylene) and its rigid derivative 5,10-dihydro-indeno(2,1-a)indene in such a scarcely perturbative solvent as 2-methylbutane on lowering the temperature revealed unfulfillment of the Mulliken–Rieke rule and the fact that, unlike its rigid derivative, t-stilbene exhibits a sort of conformational tremor that results in spectrally significant structural distortion.

Synthesis of rectangular cross-section AlN nanofibers by chemical vapor deposition by Yongbing Tang; Hongtao Cong; Zuoming Wang; Hui-Ming Cheng (171-175).
Rectangular cross-section AlN nanofibers have been synthesized by a simple chemical vapor deposition method using Al, Fe2O3 and NH3 as reactants at 800 °C. The nanofibers, which are single-crystalline hexagonal wurtzite AlN growing along [0 0 1] direction, are several hundreds of micrometers in length and 10–200 nm in width. The growth mechanism of this nanostructure at relatively low temperature was discussed, and it is revealed that Fe2O3 plays a key role in lowering the synthesis temperature. This nanofiber can be expected to serve as reinforcement for electrical packaging and structural composites, and piezoelectric nanosensors, etc.

Synthesis, structure and optical limiting property of CoII, MnII and CdII complexes with di-Schiff base and reduced di-Schiff base ligands by Ling-Yan Kong; Zhen-Wu Li; Taka-aki Okamura; Guo-Hong Ma; Qian Chu; Hui-Fang Zhu; Sing-Hai Tang; Wei-Yin Sun; Norikazu Ueyama (176-181).
Three coordination polymers [Co(L)2(SCN)2] (1), [Mn(L)2(SCN)2] (2) and [Cd(H4L)2Cl2] (3), were obtained by the reaction of CoII, MnII, CdII salts with di-Schiff base ligand N,N′-bis(3-pyridylmethyl)-4,4′-biphenylenedimethyleneimine (L) and its reduced form (H4L), respectively and their structures were determined by X-ray crystallography. In the solid state, complexes 1 and 2 feature 1D hinged chains, while complex 3 has a 2D network structure. Complex 2 was found to show optical limiting property with a 3 ns pulsed laser at 532 nm in DMF solution.

Shear-SANS study of single-walled carbon nanotube suspensions by H. Wang; G.T. Christopherson; Z.Y. Xu; L. Porcar; D.L. Ho; D. Fry; E.K. Hobbie (182-186).
We report a combined shear small-angle neutron scattering (shear-SANS) and rheo-optical study of dilute aqueous suspensions of SWNT bundles dispersed using ionic surfactants. Both shear-SANS and flow birefringence reveal weak shear-induced alignment of SWNT bundles along the direction of flow. In terms of a nematic order parameter, the degree of alignment is found to increase with the shear rate, reaching ca. 0.08 at 2000 s−1. Addition of a soluble polymer to the SWNT suspensions diminishes shear-induced alignment. The factors limiting shear alignment in dilute SWNT suspensions are discussed.

Kinetics of the gas-phase reaction of CF2 =CF–CF=CF2 with O3 and NO3 radicals by L. Chen; S. Kutsuna; K. Tokuhashi; T. Uchimaru; A. Sekiya (187-191).
The kinetics of CF2 =CF–CF=CF2 reaction with O3 (k 1) and NO3 radicals (k 2) were measured using a smog chamber/FTIR technique. The value of k 1 was determined as (1.14 ± 0.94) × 10−16  exp [−(2800 ± 225)/T] in the range 225–308 K by means of an absolute rate method and k 2 was determined to be (1.5 ± 0.2) × 10−15  cm3  molecule−1  s−1 at 298 K by a relative rate method. The tropospheric lifetime of CF2 =CF–CF=CF2 was estimated at 6.3 and 0.8 years with respect to its reaction with O3 and NO3 radicals, respectively.

To treat the field–matter interaction perturbatively, we modify the method developed by Meier and Tannor [C. Meier, D.J. Tannor, J. Chem. Phys. 111 (1999) 3365] and originally designed for propagation of reduced density matrix of systems interacting with arbitrary laser fields. Our approach is of interest to nonlinear optics. We apply this method to a simulation of transient four-wave mixing experiments for ultrafast photoinduced electron-transfer systems in a condensed phase environment. We show that such measurements are more sensitive to vibrational coherence than the electronic populations monitored in pump–probe experiments.