Vibrational Correlation Functions Research Articles

Optical Emission Spectra of Molecular Excitonic Polariton Computed at the First‐Principles Level QED‐TDDFT

In microcavity, strong coupling between light and molecules leads to the formation of hybrid excitations, i.e., the polaritons, or exciton‐polaritons. Such coupling may alter the energy landscape of the system and the optical properties of the material, making it an effective approach for controlling the light emission from molecular materials. However, due to the complexity of vibrational modes, spectroscopic calculations for organic exciton‐polaritons remain to be challenging. In this work, based on the linear‐response quantum‐electrodynamical time‐dependent density functional theory (QED‐TDDFT), we employ the thermal vibrational correlation function (TVCF) formalism to calculate the molecular optical spectrum of the lower polaritons (LP) at first‐principles level for three molecules, i.e., anthracene, distyrylbenzenes (DSB), and rubrene. The polaron decoupling effect is confirmed from our first‐principles computations. The theoretical emission spectra of LP provide fruitful insights for molecular and device design in microcavities that are otherwise hindered due to the lack of vibrational information.

Pressure effects on both fluorescent emission and charge transport properties of organic semiconductors: a computational study.

External pressure can regulate the photophysical property and charge transport performance of organic semiconductors, however, the underlying mechanism at the microscopic level is still elusive. Using thermal vibrational correlation function coupled quantum mechanics/molecular mechanics and full quantum charge transfer rate theory, we systematically explore the influence of pressure on fluorescence emission and charge transport behaviours of representative cyclooctatetrathiophene (COTh). It is found that, upon pressurization, the intramolecular configurations of COTh became more twisted, leading to the blue-shifted emission. The fluorescence quantum efficiency (FQE) of COTh crystals decreases monotonically in a wide pressure range of 0-4.38 GPa, because the increase of intermolecular electronic energy transfer rate constant (keet) is larger than the decrease of internal conversion rate constant (kic), and the variation of keet is dominant. The decrease in kic is attributed to the decreasing reorganization energy, reflecting the suppression of the low-frequency flipping vibrations of four thiophene rings and the high-frequency stretching vibrations of central cyclooctatetraene, while the keet increase is due to the simultaneous increase in exciton coupling and spectra overlap. Moreover, we predicted that the hole mobility of COTh increases monotonically by nearly an order of magnitude from 0.39 to 3.00 cm2 V-1 s-1 upon compression, because of the increase in transfer integral and the decrease of charged reorganization energy. Furthermore, its hole mobility exhibits obvious anisotropy. Our work systematically builds the external pressure, molecular packing, luminescence and transport properties relationships of organic semiconductors and provides theoretical guidance for the rational design of pressure responsive organic semiconductors with excellent photoelectric performance.

Theoretical Two Dimensional Infrared Spectroscopy of Aqueous Solutions of tert-Butyl Alcohol: Variation of the Dynamics of Spectral Diffusion along the Percolation Transition.

Binary mixtures of water and tert-butyl alcohol (TBA) are known to exhibit the so-called percolation transition where small clusters of TBA molecules span into large aggregates beyond a threshold concentration of the alcohol. In the present study, we have investigated the linear and two-dimensional infrared spectral features of aqueous solutions of TBA for varying concentration of the alcohol along the percolation transition. The percolation transition is characterized through calculations of intermolecular radial distribution functions and average size of the largest cluster of TBA molecules. It is found that, with variation of alcohol concentration, the radial distribution functions of the central carbon atoms of TBA molecules show a nonmonotonic change in the height of the first peak and also the size of the largest cluster of TBA molecules show a jump in the increase of its size for TBA mole fraction between 0.04 and 0.06 corresponding to a transition from smaller clusters to larger spanning aggregates. However, it is found that the linear infrared spectrum of water does not exhibit any noticeable changes on variation of TBA concentration along the percolation transition. Subsequently, two-dimensional infrared (2DIR) spectra and vibrational frequency time correlation function of water are calculated for all the TBA-water solutions considered in this study. The spectral diffusion of water calculated from 2DIR is found to slow down with increase of the TBA concentration. The time scales of spectral diffusion of water, as characterized by the relaxation of frequency time correlation function, 2DIR metric of central line slope, and also the hydrogen bond time correlation functions, are found to exhibit a noticeable jump along the percolation transition. The hydrophilic group of TBA is found to retard the water dynamics more effectively than the hydrophobic groups. Also, the jump in the dynamical slowdown along the percolation transition is found to be more significant for water molecules at the hydrophilic sites.

On the Importance of Well-Defined Thermal Correlation Functions in Simulating Vibronic Spectra.

Two difficulties associated with the computations of thermal vibrational correlation functions are discussed. The first one is the lack of a well-behaved expression that is valid at both high-temperature and T → 0 K limits. Specifically, if the partition function and the propagator are considered separately, then thermal vibrational correlation functions may have an indeterminate form 0/0 in the limit T → 0 K. This difficulty is resolved when the partition function and the propagator are jointly considered in the harmonic approximation, which allows a problematic term that emanates from the zero-point energy to be canceled out, thereby producing a thermal correlation function with a determinate form in the T → 0 K limit. The second difficulty is related to the multivaluedness of the vibrational correlation function. We show numerically that an improper selection of branch leads to discontinuities in the computed correlation function and incorrect vibronic spectra. We propose a phase tracking procedure that ensures continuity of both real and imaginary parts of the correlation function to recover the correct spectra. We support our findings by simulating the UV-vis absorption spectra of pentacene at 4 K and benzene at 298 K. Both are found to be in good agreement with their experimental counterparts.

Electroluminescent Mechanism of Thermally Activated Delayed Fluorescence Emitters: Conformational Effect

Recently, great progress has been made for the thermally activated delayed fluorescence (TADF) molecules. However, the electroluminescent mechanisms of TADF molecules are still not clear enough, which also impedes the development of TADF molecular materials. In this work, the electroluminescent mechanism of the TADF molecule 2,5-di((9H-carbazol-9-yl)phenyl)(pyridin-4-yl)methanone (DCBPy) is studied theoretically. Four stable conformers (A, B, C, and D) are found for the DCBPy molecule based on first-principles calculation. The decay rates of excited states for all the four conformers are calculated using the thermal vibrational correlation function method. It is found that conformers A and B are higher in energy than conformers C and D (with significant intramolecular interaction), so conformers C and D are the dominant configurations based on Boltzmann distribution analysis. The emission wavelengths of C and D, which are in good agreement with experimental values, are blue-shift than those of A and B. Th...

Raman band shape analysis of cyanate-anion ionic liquids

Raman band shape analysis of the C≡N stretching mode was carried out for ionic liquids based on [SCN]−, [N(CN)2]−, [C(CN)3]−, and [B(CN)4]−, with a common cation, 1-ethyl-3-methylimidazolium, [C2C1im]+. Vibrational and reorientational time correlation functions were obtained by Fourier transforming isotropic and anisotropic Raman spectra. Comparison is provided between results for [C2C1im][SCN] and literature data available for molten alkali thiocyanates. Vibrational dephasing of the ωCN mode in [C2C1im][SCN] belongs to the regime of inhomogeneous broadening as it is determined by the distribution of vibrational frequencies, <Δω2>. Vibrational dephasing in [N(CN)2]−, [C(CN)3]−, and [B(CN)4]−, depends on both the <Δω2> and the correlation time of frequency fluctuation. Decay rates of reorientational time correlation functions within the range of 1.0ps do not correlate with the viscosity of these ionic liquids. Molecular dynamics simulations of these ionic liquids provide support to the experimental finding that the reorientational time correlation function of [SCN]− decays faster than the other anions. The Raman band shape analysis suggests that the short-time dynamics of these ionic liquids is structure-limited because of steric hindrance.

Computational Evaluation of Optoelectronic Properties for Organic/Carbon Materials

CONSPECTUS: Organic optoelectronic materials are used in a variety of devices, including light-emitting diodes, field-effect transistors, photovoltaics, thermoelectrics, spintronics, and chemico- and biosensors. The processes that determine the intrinsic optoelectronic properties occur either in the photoexcited states or within the electron-pumped charged species, and computations that predict these optical and electrical properties would help researchers design new materials. In this Account, we describe recent advances in related density functional theory (DFT) methods and present case studies that examine the efficiency of light emission, carrier mobility, and thermoelectric figures of merit by calculation of the electron-vibration couplings. First we present a unified vibrational correlation function formalism to evaluate the excited-state radiative decay rate constant kr, the nonradiative decay rate constant knr, the intersystem crossing rate constant kISC, and the optical spectra. The molecular parameters that appear in the formalism, such as the electronic excited-state energy, vibrational modes, and vibronic couplings, require extensive DFT calculations. We used experiments for anthracene at both low and ambient temperatures to benchmark the calculated photophysical parameters. In the framework of Fermi's golden rule, we incorporated the non-adiabatic coupling and the spin-orbit coupling to evaluate the phosphorescence efficiency and emission spectrum. Both of these are in good agreement with experimental results for anthracene and iridium compounds. Band electron scattering and relaxation processes within Boltzmann theory can describe charge transport in two-dimensional carbon materials and closely packed organic solids. For simplicity, we considered only the acoustic phonon scattering as modeled by the deformation potential approximation coupled with extensive DFT calculations for band structures. We then related the carrier mobility to the band-edge shift associated with the lattice dilation of longitudinal waves. The calculated relaxation time was in good agreement with experimental data for the graphene sheet, which supports the methodology. We then found that the intrinsic electron mobility for a 6,6,12-graphyne sheet can be even larger than that of graphene. We extended this approach to investigate the thermoelectric transport of electrons in metal phthalocyanines, which showed reasonable Seebeck coefficients when compared with experiments. For the thermal lattice transport, we employed nonequilibrium molecular dynamics simulations. Combining both electron transport and lattice thermal conductivity, we can evaluate the thermoelectric figure of merit.

Liquid phase dynamics of molten M2S2O7 (M = K, Cs): A temperature dependent Raman spectroscopic study

The dynamics of M2S2O7 (M=K, Cs) pyrosulfate salts in the liquid state is investigated by steady-state Raman spectroscopic experiments performed at temperatures up to 600°C. The symmetric stretching modes of the S2O72− ions have been used as probes of the dynamics of these melts. Contrary to the most previous picosecond dynamics studies performed by means of Raman line profile analysis, we have employed in this work an approach that enables the extraction of valuable information concerning short-time dynamics by calculating time correlation functions of vibrational relaxation by fits in the frequency domain. The fitting method used enables the modeling of the real line profiles in a manner that is intermediate between Lorentzian and Gaussian by means of a function, which has an analytical counterpart in the time domain. The vibrational time correlation functions for both molten salts studied are rather adequately interpreted within the assumption of exponential modulation function concerning the environmental modulation in the context of Kubo–Rothschild approach and indicate that the system experiences an intermediate dynamical regime that gets only slower with increasing temperature. Continuous temperature dependence of the dephasing parameters is observed, while the temperature dependence of the dispersion parameter α indicates deviation from the simple liquid model and offers a complete picture of the way a complex liquid attains the condition of a simple one. The evolution of the dispersion parameter is indicative of the reduction of the coherence decay in the perturbation potential as a consequence of local short-lived aggregates. The experimental results are discussed in terms of theoretical models providing insight in the intermolecular coupling mechanisms.

Site-Specific Coupling of Hydration Water and Protein Flexibility Studied in Solution with Ultrafast 2D-IR Spectroscopy

There is considerable evidence for the slaving of biomolecular dynamics to the motions of the surrounding solvent environment, but to date there have been few direct experimental measurements capable of site-selectively probing both the dynamics of the water and the protein with ultrafast time resolution. Here, two-dimensional infrared spectroscopy (2D-IR) is used to study the ultrafast hydration and protein dynamics sensed by a metal carbonyl vibrational probe covalently attached to the surface of hen egg white lysozyme dissolved in D(2)O/glycerol solutions. Surface labeling provides direct access to the dynamics at the protein-water interface, where both the hydration and the protein dynamics can be observed simultaneously through the vibrational probe's frequency-frequency correlation function. In pure D(2)O, the correlation function shows a fast initial 3 ps decay corresponding to fluctuations of the hydration water, followed by a significant static offset attributed to fluctuations of the protein that are not sampled within the <20 ps experimental window. Adding glycerol increases the bulk solvent viscosity while leaving the protein structurally intact and hydrated. The hydration dynamics exhibit a greater than 3-fold slowdown between 0 and 80% glycerol (v/v), and the contribution from the protein's dynamics is found to slow in a nearly identical fashion. In addition, the magnitude of the dynamic slowdown associated with hydrophobic hydration is directly measured and shows quantitative agreement with predictions from molecular dynamics simulations.

Short-time microscopic dynamics of aqueous methanol solutions

In this paper we present the picosecond vibrational dynamics of a series of methanol aqueous solutions over a wide concentration range from dense to dilute solutions. We studied the vibrational dephasing and vibrational frequency modulation by calculating the time correlation functions of vibrational relaxation by fits in the frequency domain. This method is applied to aqueous methanol solutions xMeOH–(1 − x)H2O, where x = 0, 0.2, 0.4, 0.6, 0.8 and 1. The important finding is that the vibrational dynamics of the system become slower with increasing methanol concentration. The removal of many-body effects by having the molecules in less-crowded environments seems to be the key factor. The interpretation of the vibrational correlation function in the context of Kubo theory, which is based on the assumption that the environmental modulation arises from a single relaxation process and applied to simple liquids, is inadequate for all solutions studied. We found that the vibrational correlation functions of the solutions over the whole concentration range comply with the Rothschild approach, assuming that the environmental modulation is described by a stretched exponential decay. The evolution of the dispersion parameter α with dilution indicates the deviation of the solutions from the model simple liquid and the results are discussed in the framework of the current phenomenological status of the field.

Picosecond dynamics from lanthanide chloride melts

The picosecond dynamics of molten lanthanide chlorides is studied by means of vibrational spectroscopy. Polarized Raman spectra of molten LaCl3, NdCl3, GdCl3, DyCl3, HoCl3 and YCl3 are fitted to a model enabling to obtain the times of vibrational dephasing, tν and vibrational frequency modulation tω. Our aim is to find possible sensitive indicators of short-time dynamics. It has been found that all lanthanide chlorides exhibit qualitative similarities in the vibrational relaxation and frequency modulation times in the molten state. It appears that the vibrational correlation functions of all melts comply with the Rothschild approach assuming that the environmental modulation is described by a stretched exponential decay. The evolution of the dispersion parameter α indicates the deviation of the melts from the model simple liquid and the similar local environment in which the oscillator is placed and with which it is coupled. The “packing” of the anions around central La3+ cation seems to be the key factor for the structure and the dynamics of the melts. The results are discussed in the framework of the current phenomenological status of the field.

Rotational dynamics of solvated carbon dioxide studied by infrared, Raman, and time-resolved infrared spectroscopies and a molecular dynamics simulation

Rotational dynamics of solvated carbon dioxide (CO(2)) has been studied. The infrared absorption band of the antisymmetric stretch mode in acetonitrile is found to show a non-Lorentzian band shape, suggesting a non-exponential decay of the vibrational and/or rotational correlation functions. A combined method of a molecular dynamics (MD) simulation and a quantum chemical calculation well reproduces the observed band shape. The analysis suggests that the band broadening is almost purely rotational, while the contribution from the vibrational dephasing is negligibly small. The non-exponential rotational correlation decay can be explained by a simple rotor model simulation, which can treat large angle rotations of a relatively small molecule. A polarized Raman study of the symmetric stretch mode in acetonitrile gives a rotational bandwidth consistent with that obtained from the infrared analysis. A sub-picosecond time-resolved infrared absorption anisotropy measurement of the antisymmetric stretch mode in ethanol also gives a decay rate that is consistent with the observed rotational bandwidths.

Short-time vibrational dynamics of metaphosphate glasses

In this paper we present the picosecond vibrational dynamics of a series of binary metaphosphate glasses, namely Na 2O–P 2O 5, MO–P 2O 5 (M=Ba, Sr, Ca, Mg) and Al 2O 3–3P 2O 5 by means of Raman spectroscopy. We studied the vibrational dephasing and vibrational frequency modulation by calculating time correlation functions of vibrational relaxation by fits in the frequency domain. The fitting method used enables one to model the real line profiles intermediate between Lorentzian and Gaussian by an analytical function, which has an analytical counterpart in the time domain. The symmetric stretching modes ν s (PO 2 −) and ν s (P–O–P) of the PO 2 − entity of PØ 2O 2 − units and of P–O–P bridges in metaphosphate arrangements have been investigated by Raman spectroscopy and we used them as probes of the dynamics of these glasses. The vibrational time correlation functions of both modes studied are rather adequately interpreted within the assumption of exponential modulation function in the context of Kubo–Rothschield theory and indicate that the system experiences an intermediate dynamical regime that gets only slower with an increase in the ionic radius of the cation-modifier. We found that the vibrational correlation functions of all glasses studied comply with the Rothschild approach assuming that the environmental modulation is described by a stretched exponential decay. The evolution of the dispersion parameter α with increasing ionic radius of the cation indicates the deviation from the model simple liquid indicating the reduction of the coherence decay in the perturbation potential as a result of local short lived aggregates. The results are discussed in the framework of the current phenomenological status of the field.

General mapping between random walks and thermal vibrations in elastic networks: Fractal networks as a case study

We present an approach to mapping between random walks and vibrational dynamics on general networks. Random walk occupation probabilities, first passage time distributions and passage probabilities between nodes are expressed in terms of thermal vibrational correlation functions. Recurrence is demonstrated equivalent to the Landau-Peierls instability. Fractal networks are analyzed as a case study. In particular, we show that the spectral dimension governs whether or not the first passage time distribution is well represented by its mean. We discuss relevance to universal features arising in protein vibrational dynamics.

Raman Spectroscopic Studies of Liquid Phase Ordering and Dynamics for Solutions of ME6N Liquid Crystal: The Approach to Simple Molecule Behavior at High Dilutions

We have measured the Raman isotropic profiles of the ν(C≡N) band at 2235 cm(-1) for five solutions of ME6N (4-cyanophenyl-4'-hexylbenzoate) liquid crystal dissolved in CCl(4) in the range from x = 0.12 to 0.007 (x, mole fraction of ME6N) and then obtained the corresponding vibrational correlation functions, C(v)(t), by time Fourier transformation. The increase with dilution of the dephasing times τ(v) complies with the behavior of the nonmonotonic concentration dependence predicted by the fluctuation concentration model for this concentration range (x < 0.5). The interpretation of C(v)(t) within the Kubo stochastic theory which, being based on the assumption that the environmental modulation arises from a single relaxation process, e(-t/τ(c)), applies to simple liquids, has proved to be inadequate except for the most diluted solutions where the environmental correlation time τ(c) amounted to 1.16 ps. On the other hand, we have found that the vibrational correlation functions for these ME6N/CCl(4) solutions comply, in the whole concentration range, with the approach proposed by Rothschild, which, being based on the assumption that the environmental modulation is described by a stretched exponential decay e(-(t/τ(0))(α)), is more appropriate for the interpretation of the vibrational correlation function arising from a distribution of relaxation processes caused, as in the present case, by the persistence of pseudonematic domains. With dilution the dispersion parameter α and the average correlation time τ(0) progressively increases and decreases, respectively, and tend to converge to the values appropriate for simple liquids, as given by the Kubo theory, i.e., α to unity and τ(0) to approximately 1.16 ps. The relaxation time probability distribution h(τ) progressively shrinks and shifts down with dilution. The evolution of α and τ(0) parameters and, contextually, of h(τ) with dilution offers a complete picture of the way a complex liquid attains the condition of a simple one.

Hydrogen Bond Rearrangements in Water Probed with Temperature-Dependent 2D IR

We use temperature-dependent two-dimensional infrared spectroscopy (2D IR) of dilute HOD in H2O to investigate hydrogen bond rearrangements in water. The OD stretching frequency is sensitive to its environment, and loss of frequency correlation provides a picture of local and collective hydrogen bond dynamics. The time scales for hydrogen bond rearrangements decrease from roughly 2 ps at 278 K to 0.5 ps at 345 K. We find the barrier to dephasing and hydrogen bond switching to be Ea = 3.4 ± 0.5 kcal/mol, although the trend is slightly non-Arrhenius. The value is in good agreement with the reported barrier height for OD reorientation observed in pump−probe anisotropy measurements. This provides evidence for the proposal that hydrogen bond switching occurs through concerted large angular jump reorientation. MD simulations of temperature-dependent OD vibrational dephasing and orientational correlation functions are used to support our conclusions.

Time-correlation function approach to molecular anharmonicity in hyperthermal atom-molecule collisions

In hyperthermal atom-molecule collisions, differential cross sections for vibrational and rotational excitation are related to correlation functions of the positions of the atoms that constitute the target. We present a new approach to the evaluation of the correlation functions that encompasses the effects of anharmonic vibrations of the polyatomic. By means of cumulant expansion techniques, the vibrational correlation function is expressed in terms of displacement—displacement correlation functions, which are obtained from the corresponding double-time Green functions. The displacement-displacement Green functions are evaluated by decoupling their hierarchy of equations of motion with a linearization procedure that includes anharmonic forces to infinite order. Results for cubic and quartic anharmonicities in N2, CO, and in the bending mode of CO2 indicate that, at hyperthermal collision energies, anharmonic forces contribute less than 1% to the vibrational energy transferred to these targets.

Integrated and dispersed photon echo studies of nitrile stretching vibration of 4-cyanophenol in methanol

By means of integrated and dispersed IR photon echo measurement methods, the vibrational dynamics of C-N stretch modes in 4-cyanophenol and 4-cyanophenoxide in methanol is investigated. The vibrational frequency-frequency correlation function (FFCF) is retrieved from the integrated photon echo signals by assuming that the FFCF is described by two exponential functions with about 400 fs and a few picosecond components. The excited state lifetimes of the C-N stretch modes of neutral and anionic 4-cyanophenols are 1.45 and 0.91 ps, respectively, and the overtone anharmonic frequency shifts are 25 and 28 cm(-1). At short waiting times, a notable underdamped oscillation, which is attributed to a low-frequency intramolecular vibration coupled to the CN stretch, in the integrated and dispersed vibrational echo as well as transient grating signals was observed. The spectral bandwidths of IR absorption and dispersed vibrational echo spectra of the 4-cyanophenoxide are significantly larger than those of its neutral form, indicating that the strong interaction between phenoxide and methanol causes large frequency fluctuation and rapid population relaxation. The resonance effects in a paradisubstituted aromatic compound would be of interest in understanding the conjugation effects and their influences on chemical reactivity of various aromatic compounds in organic solvents.

Beyond the Förster theory of excitation energy transfer: importance of higher-order processes in supramolecular antenna systems

Electronic excitation energy transfer in molecular systems is connected with the de-excitation of one molecule and the excitation of the other. Mostly, it can be understood in terms of Förster (or fluorescence) resonance energy transfer. An increasing interest in the optimization of artificial light harvesting systems, however, requires a more detailed study going beyond the standard Förster scheme. There are two main routes to do this. Considering a Coulombic less-strongly coupled system first, coherences among different chromophores may be considered in the framework of perturbation theory with higher-order mechanisms correcting the standard second-order description. Secondly, if inter-chromophore coherences are dominant and delocalized Frenkel-exciton states are formed, it becomes of some importance to study their decay due to the coupling to vibrational degrees of freedom. While we will also comment on this latter mechanism, the first description based on localized excitations will be the main focus. A general higher-order theory resulting in respective transition rates and rate equations is utilized. Its capability is demonstrated when presenting a systematic description of short-range and long-range corrections to the basic Förster mechanism. Accordingly, a unique description of bridge-mediated and photon-mediated long-range electronic excitation energy transfer is offered. Moreover, short-range excitation energy transfer appearing as a two electron exchange is also discussed. And, the exciton-exciton annihilation process present at higher optical excitation intensities is described as a direct higher-order transition. The related higher-order vibrational correlation functions are presented and estimated for the reference case where the coupling to vibrational degrees of freedom either of intra-molecular or inter-molecular type is reduced to a simple electronic state dephasing process.

Frequency-frequency correlation functions and apodization in two-dimensional infrared vibrational echo spectroscopy: A new approach

Ultrafast two-dimensional infrared (2D-IR) vibrational echo spectroscopy can probe structural dynamics under thermal equilibrium conditions on time scales ranging from femtoseconds to approximately 100 ps and longer. One of the important uses of 2D-IR spectroscopy is to monitor the dynamical evolution of a molecular system by reporting the time dependent frequency fluctuations of an ensemble of vibrational probes. The vibrational frequency-frequency correlation function (FFCF) is the connection between the experimental observables and the microscopic molecular dynamics and is thus the central object of interest in studying dynamics with 2D-IR vibrational echo spectroscopy. A new observable is presented that greatly simplifies the extraction of the FFCF from experimental data. The observable is the inverse of the center line slope (CLS) of the 2D spectrum. The CLS is the inverse of the slope of the line that connects the maxima of the peaks of a series of cuts through the 2D spectrum that are parallel to the frequency axis associated with the first electric field-matter interaction. The CLS varies from a maximum of 1 to 0 as spectral diffusion proceeds. It is shown analytically to second order in time that the CLS is the T(w) (time between pulses 2 and 3) dependent part of the FFCF. The procedure to extract the FFCF from the CLS is described, and it is shown that the T(w) independent homogeneous contribution to the FFCF can also be recovered to yield the full FFCF. The method is demonstrated by extracting FFCFs from families of calculated 2D-IR spectra and the linear absorption spectra produced from known FFCFs. Sources and magnitudes of errors in the procedure are quantified, and it is shown that in most circumstances, they are negligible. It is also demonstrated that the CLS is essentially unaffected by Fourier filtering methods (apodization), which can significantly increase the efficiency of data acquisition and spectral resolution, when the apodization is applied along the axis used for obtaining the CLS and is symmetrical about tau=0. The CLS is also unchanged by finite pulse durations that broaden 2D spectra.