In this paper different floating oscillator models for describing the amide I band of peptides and proteins are compared with density functional theory (DFT) calculations. Models for the variation of the frequency shifts of the oscillators and the nearest-neighbor coupling between them with respect to conformation are constructed from DFT normal mode calculations on N-acetyl-glycine-N′-methylamide. The calculated frequencies are compared with those obtained from existing electrostatic models. Furthermore, a new transition charge coupling model is presented. We suggest a model which combines the nearest-neighbor maps with long-range interactions accounted for using the new transition charge model and an existing electrostatic map for long-range interaction frequency shifts. This model and others, which account for the frequency shifts by electrostatic maps exclusively, are tested by comparing the predicted IR spectra with those from DFT calculations on the pentapeptide [Leu]-enkephalin. The new model described above gives the best agreement and, after a systematic blueshift is accounted for, reproduces the DFT frequencies to within 3.5cm−1. The correlation of the intensities for this model with intensities from DFT calculations is 0.94.

Vibrational spectroscopy is an essential tool in chemical analyses, biological assays, and studies of functional materials. Over the past decade, various coherent nonlinear vibrational spectroscopic techniques have been developed and enabled researchers to study time-correlations of the fluctuating frequencies that are directly related to solute-solvent dynamics, dynamical changes in molecular conformations and local electrostatic environments, chemical and biochemical reactions, protein structural dynamics and functions, characteristic processes of functional materials, and so on. In order to gain incisive and quantitative information on the local electrostatic environment, molecular conformation, protein structure and inter-protein contacts, ligand binding kinetics, and electric and optical properties of functional materials, a variety of vibrational probes have been developed and site-specifically incorporated into molecular, biological, and material systems for time-resolved vibrational spectroscopic investigation. However, still, an allencompassing theory that describes the vibrational solvatochromism, electrochromism, and dynamic fluctuation of vibrational frequencies has not been completely established mainly due to the intrinsic complexity of intermolecular interactions in condensed phases. In particular, the amount of data obtained from the linear and nonlinear vibrational spectroscopic experiments has been rapidly increasing, but the lack of a quantitative method to interpret these measurements has been one major obstacle in broadening the applications of these methods. Among various theoretical models, one of the most successful approaches is a semi-empirical model generally referred to as the vibrational spectroscopic map that is based on a rigorous theory of intermolecular interactions. Recently, genetic algorithm, neural network, and machine learning approaches have been applied to the development of vibrational solvatochromism theory. In this review, we provide comprehensive descriptions of the theoretical foundation and various examples showing its extraordinary successes in the interpretations of experimental observations. In addition, a brief introduction to a newly created repository website (http://frequencymap.org) for vibrational spectroscopic maps is presented. We anticipate that a combination of the vibrational frequency map approach and state-of-theart multidimensional vibrational spectroscopy will be one of the most fruitful ways to study the structure and dynamics of chemical, biological, and functional molecular systems in the future.

A complete treatment of the entanglement of two-level systems, which evolves through the contact with a thermal bath, must include the fact that the system and the bath are not fully separable. Therefore, quantum coherent superpositions of system and bath states, which are almost never fully included in theoretical models, are invariably present when an entangled state is prepared experimentally. We show their importance for the time evolution of the entanglement of two qubits coupled to independent baths. In addition, our treatment is able to handle slow and low-temperature thermal baths.The crucial feature of quantum information is the presence of coherent superpositions. A single isolated twolevel system (qubit) can be prepared in a superposition of its 0 and 1 states, and the manipulation of such states leads to new possibilities for the storage and processing of information. In a pure quantum system, the superposition is entirely coherent, which means that a definite phase relation exists between the 0 and 1 states. Unlike in the ideal isolated case, the interactions of real quantum systems with their environment lead to the destruction of these phase relations, in other words, decoherence.More interesting than a single two-level system is a collection of multiple such qubits. Coherent superposition states of multiple qubits can be prepared, and their dynamics are studied to understand the functioning of quantum networks.1 The presence of phase relations between qubits, a second type of coherence, is termed entanglement. The destruction of entanglement through interactions with the environment is an important problem, both for a fundamental understanding of quantum mechanics and the development of quantum information processing.2 Recently, it has been found that the decay of entanglement can be very different from that of the single qubit coherence. In particular, the entanglement can disappear completely in finite time.3 Interactions between qubits further affect the time scale of the decay. Here, we argue that, besides single qubit coherence and the entanglement of multiple qubits, there is a third form of coherence that is important for the description of quantum information. The physical nature of this effect lies in a detailed description of the heat bath that leads to decoherence and disentanglement. In a complete theory, both the system and the bath are quantum mechanical. It is therefore possible, and often unavoidable in experiment, to create coherent superpositions of system and bath states, and such superpositions will play an important role in the time evolution of the qubit system of interest.The description of entanglement dynamics starts from an equation of motion for the qubits together with an initial condition, which are both affected by a correct description of the bath. Most theoretical treatments, including the Redfield and Lindblad formulations, describe the qubit dynamics under the Born and ultrafast bath approximations.5 These lead to convenient timelocal equations of motion, but are...

Criteria for the accuracy of small polaron quantum master equation in simulating excitation energy transfer dynamics J. Chem. Phys. 139, 224112 (2013) (2014)], we go beyond the commonly used Born-Markov approximations to incorporate system-environment correlations and the resultant non-Markovian dynamical effects. We obtain energy transfer dynamics for both underdamped and overdamped oscillator environments that are in perfect agreement with the numerical hierarchical equations of motion over a wide range of parameters. Furthermore, we show that the Zusman equations, which may be obtained in a semiclassical limit of the reaction coordinate model, are often incapable of describing the correct dynamical behaviour. This demonstrates the necessity of properly accounting for quantum correlations generated between the system and its environment when the Born-Markov approximations no longer hold. Finally, we apply the reaction coordinate formalism to the case of a structured environment comprising of both underdamped (i.e., sharply peaked) and overdamped (broad) components simultaneously. We find that though an enhancement of the dimer energy transfer rate can be obtained when compared to an unstructured environment, its magnitude is rather sensitive to both the dimer-peak resonance conditions and the relative strengths of the underdamped and overdamped contributions. C 2016 AIP Publishing LLC. [http://dx