The frequency fluctuation correlation function (FFCF) measures the spectral diffusion of a state's transition while the frequency fluctuation cross-correlation function (FXCF) measures the correlation dynamics between the transitions of two separate states. These quantities contain a wealth of information on how the chromophores or excitonic states interact and couple with its environment and with each other. We summarize the experimental implementations and theoretical considerations of using two-dimensional electronic spectroscopy to characterize FFCFs and FXCFs. Applications can be found in systems such as the chlorophyll pigment molecules in light-harvesting complexes and CdSe nanomaterials.
In a two-dimensional (2D) optical spectrum of a multilevel system, there are diagonal peaks and off-diagonal cross-peaks that correlate the different levels. The time-dependent properties of these diagonal peaks and cross-peaks contain much information about the dynamics of the multilevel system. The time-dependent diagonal peakshape that depends on the spectral diffusion dynamics of the associated transition and characterized by the frequency-fluctuation correlation function (FFCF) is well studied. However, the time-dependent peakshape of a cross-peak that provides the correlation dynamics between different transitions is much less studied or understood. We derived the third-order nonlinear response functions that describe the cross-peaks in a 2D electronic spectrum of a multilevel system that arise from processes sharing a common ground state and/or from internal conversion and population transfer. We can use the center line slope (CLS) analysis to characterize the cross-peaks in conjunction with the diagonal peaks. This allows us to recover the frequency-fluctuation cross-correlation functions (FXCFs) between two transitions. The FXCF and its subsidiary quantities such as the initial correlation and the initial covariance between different transitions are important for studying the correlation effects between states in complex systems, such as energy-transfer processes. Furthermore, knowledge of how various molecular processes over different timescales affect simultaneously different transitions can also be obtained from the measured FXCF. We validated and tested our derived equations and analysis process by studying, as an example, the 2D electronic spectra of metal-free phthalocyanine in solution. We measured and analyzed the diagonal peaks of the Qx and Qy transitions and the cross-peaks between these two transitions of this multilevel electronic system and obtained the associated FFCFs and FXCFs. In this model system, we measured negative components of FXCF over the tens of picosecond timescale. This suggests that in phthalocyanine, the Qx and Qy transitions coupling with the solvent molecule motion are anticorrelated to each other.
High blood pressure is the leading modifiable risk factor for mortality, accounting for nearly 1 in 5 deaths worldwide and 1 in 11 in low-income countries. Hypertension control remains a challenge, especially in low-resource settings. One approach to improvement is the prioritization of patient-centered care. However, consensus on the outcomes that matter most to patients is lacking. We aimed to define a standard set of patient-centered outcomes for evaluating hypertension management in low- and middle-income countries. The International Consortium for Health Outcomes Measurement convened a Working Group of 18 experts and patients representing 15 countries. We used a modified Delphi process to reach consensus on a set of outcomes, case-mix variables, and a timeline to guide data collection. Literature reviews, patient interviews, a patient validation survey, and an open review by hypertension experts informed the set. The set contains 18 clinical and patient-reported outcomes that reflect patient priorities and evidence-based hypertension management and case-mix variables to allow comparisons between providers. The domains included are hypertension control, cardiovascular complications, health-related quality of life, financial burden of care, medication burden, satisfaction with care, health literacy, and health behaviors. We present a core list of outcomes for evaluating hypertension care. They account for the unique challenges healthcare providers and patients face in low- and middle-income countries, yet are relevant to all settings. We believe that it is a vital step toward international benchmarking in hypertension care and, ultimately, value-based hypertension management.