An effective potential for Frenkel excitons.

Excitation energy transfer (EET) is a ubiquitous process in life and materials sciences. Here, a new and computationally efficient method of evaluating the electronic EET couplings between interacting chromophores is introduced that is valid in a wide range of intermolecular distances. The proposed approach is based on the effective elimination of electron repulsion integrals from the excitonic Hamiltonian matrix elements via the density-fitting approach and distributed multipole approximation. The excitonic Hamiltonian represented in a basis including charge transfer (CT) states is re-cast in terms of the effective one-electron potential functions (EOPs) and adapted into the effective fragment parameter (EFP) framework. Calculations for model systems indicate that the speedup of at least three orders of magnitude, as compared to the state-of-the-art methods, can be achieved while maintaining the accuracy of the EET couplings even at short intermolecular distances.

Ab initio effective one-electron potential operators: Applications for charge-transfer energy in effective fragment potentials.

The concept of effective one-electron potentials (EOPs) has proven to be extremely useful in efficient description of electronic structure of chemical systems, especially extended molecular aggregates such as interacting molecules in condensed phases. Here, a general method for EOP-based elimination of electron repulsion integrals is presented, that is tuned toward the fragment-based calculation methodologies such as the second generation of the effective fragment potentials (EFP2) method. Two general types of the EOP operator matrix elements are distinguished and treated either via the distributed multipole expansion or the extended density fitting (DF) schemes developed in this work. The EOP technique is then applied to reduce the high computational costs of the effective fragment charge-transfer (CT) terms being the bottleneck of EFP2 potentials. The alternative EOP-based CT energy model is proposed, derived within the framework of intermolecular perturbation theory with Hartree-Fock noninteracting reference wavefunctions, compatible with the original EFP2 formulation. It is found that the computational cost of the EFP2 total interaction energy calculation can be reduced by up to 38 times when using the EOP-based formulation of CT energy, as compared to the original EFP2 scheme, without compromising the accuracy for a wide range of weakly interacting neutral and ionic molecular fragments. The proposed model can thus be used routinely within the EFP2 framework.

Vibrational Spectroscopic Map, Vibrational Spectroscopy, and Intermolecular Interaction.

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 interprotein 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 all-encompassing 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 semiempirical 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 Web site (http://frequencymap.org) for vibrational spectroscopic maps is presented. We anticipate that a combination of the vibrational frequency map approach and state-of-the-art 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.

Vibrational Lifetime of the SCN Protein Label in H2O and D2O Reports Site-Specific Solvation and Structure Changes During PYP's Photocycle.

The application of vibrational labels such as thiocyanate  (-S-C≡N) for studying protein structure and dynamics is thriving. Absorption spectroscopy is usually employed to obtain wavenumber and line shape of the label. An observable of great significance might be the vibrational lifetime, which can be obtained by pump probe or 2D-IR spectroscopy. Due to the insulating effect of the heavy sulfur atom in the case of the SCN label, the lifetime of the C≡N oscillator is expected to be particularly sensitive to its surrounding as it is not dominated by through-bond relaxation. We therefore investigate the vibrational lifetime of the SCN label at various positions in the blue light sensor protein Photoactive Yellow Protein (PYP) in the ground state and signaling state of the photoreceptor. We find that the vibrational lifetime of the C≡N stretching mode is strongly affected both by its protein environment and by the degree of exposure to the solvent. Even for label positions where the line shape and wavenumber observed by FTIR are barely changing upon activation of the photoreceptor, we find that the lifetime can change considerably. To obtain an unambiguous measure for the solvent exposure of the labeled site, we show that it is imperative to compare the lifetimes in H2O and D2O. Importantly, the lifetimes shorten in H2O as compared to D2O for water exposed labels, while they stay largely the same for buried labels. We quantify this effect by defining a solvent exclusion coefficient (SEC). The response of the label's vibrational lifetime to its solvent exposure renders it a suitable universal probe for protein investigations. This applies even to systems that are otherwise hard to address, such as transient or short-lived states, which could be created during a protein's working cycle (as here in PYP) or during protein folding. It is also applicable to flexible systems (intrinsically disordered proteins), protein-protein and protein-membrane interactions.

Following local light-induced structure changes and dynamics of the photoreceptor PYP with the thiocyanate IR label.

Photoactive Yellow Protein (PYP) is a bacterial blue light receptor that enters a photocycle after excitation. The intermediate states are formed on time scales ranging from femtoseconds up to hundreds of milliseconds, after which the signaling state with a lifetime of about 1 s is reached. To investigate structural changes and dynamics, we incorporated the SCN IR label at distinct positions of the photoreceptor via cysteine mutation and cyanylation. FT-IR measurements of the SCN label at different sites of the well-established dark state structure of PYP characterized the spectral response of the label to differences in the environment. Under constant blue light irradiation, we observed the formation of the signaling state with significant changes of wavenumber and lineshape of the SCN bands. Thereby we deduced light-induced structural changes in the local environment of the labels. These results were supported by molecular dynamics simulations on PYP providing the solvent accessible surface area (SASA) at the different positions. To follow protein dynamics via the SCN label during the photocycle, we performed step-scan FT-IR measurements with a time resolution of 10 µs. Global analysis yielded similar time constants of τ1 = 70 µs, τ2 = 640 µs, and τ3 > 20 ms for the wild type and τ1 = 36 µs, τ2 = 530 µs, and τ3 > 20 ms for the SCN-labeled mutant PYP-A44C*, a mutant which provided a sufficiently large SCN difference signal to measure step-scan FT-IR spectra. In comparison to the protein (amide, E46) and chromophore bands the dynamics of the SCN label show a different behavior. This result indicates that the local kinetics sensed by the label are different from the global protein kinetics.

One-particle density matrix polarization susceptibility tensors.

The electric field-induced change in the one-electron density has been expressed as a series of the one-particle density matrix susceptibilities interacting with the spatial distribution of the electric field. The analytic approximate expressions are derived at the Hartree-Fock theory, which serves as a basis for the construction of the generalized model that is designed for an arbitrary form of wavefunction and any type of one-particle density matrix. It is shown that it is possible to accurately predict the changes in the one-electron ground-state density of water molecule in a spatially uniform electric field, as well as in spatially non-uniform electric field distribution generated by point charges. When both linear and quadratic terms with respect to the electric field are accounted for, the electric field-induced polarization energies, dipole moments, and quadrupole moments are quantitatively described by the present theory in electric fields ranging from weak to very strong (0.001-0.07 a.u.). It is believed that the proposed model could open new routes in quantum chemistry for fast and efficient calculations of molecular properties in condensed phases.

A Direct, Quantitative Connection between Molecular Dynamics Simulations and Vibrational Probe Line Shapes.

A quantitative connection between molecular dynamics simulations and vibrational spectroscopy of probe-labeled systems would enable direct translation of experimental data into structural and dynamical information. To constitute this connection, all-atom molecular dynamics (MD) simulations were performed for two SCN probe sites (solvent-exposed and buried) in a calmodulin-target peptide complex. Two frequency calculation approaches with substantial nonelectrostatic components, a quantum mechanics/molecular mechanics (QM/MM)-based technique and a solvatochromic fragment potential (SolEFP) approach, were used to simulate the infrared probe line shapes. While QM/MM results disagreed with experiment, SolEFP results matched experimental frequencies and line shapes and revealed the physical and dynamic bases for the observed spectroscopic behavior. The main determinant of the CN probe frequency is the exchange repulsion between the probe and its local structural neighbors, and there is a clear dynamic explanation for the relatively broad probe line shape observed at the "buried" probe site. This methodology should be widely applicable to vibrational probes in many environments.

Vibrational Probes: From Small Molecule Solvatochromism Theory and Experiments to Applications in Complex Systems.

The vibrational frequency of a chosen normal mode is one of the most accurately measurable spectroscopic properties of molecules in condensed phases. Accordingly, infrared absorption and Raman scattering spectroscopy have provided valuable information on both distributions and ensemble-average values of molecular vibrational frequencies, and these frequencies are now routinely used to investigate structure, conformation, and even absolute configuration of chemical and biological molecules of interest. Recent advancements in coherent time-domain nonlinear vibrational spectroscopy have allowed the study of heterogeneous distributions of local structures and thermally driven ultrafast fluctuations of vibrational frequencies. To fully utilize IR probe functional groups for quantitative bioassays, a variety of biological and chemical techniques have been developed to site-specifically introduce vibrational probe groups into proteins and nucleic acids. These IR-probe-labeled biomolecules and chemically reactive systems are subject to linear and nonlinear vibrational spectroscopic investigations and provide information on the local electric field, conformational changes, site-site protein contacts, and/or function-defining features of biomolecules. A rapidly expanding library of data from such experiments requires an interpretive method with atom-level chemical accuracy. However, despite prolonged efforts to develop an all-encompassing theory for describing vibrational solvatochromism and electrochromism as well as dynamic fluctuations of instantaneous vibrational frequencies, purely empirical and highly approximate theoretical models have often been used to interpret experimental results. They are, in many cases, based on the simple assumption that the vibrational frequency of an IR reporter is solely dictated by electric potential or field distribution around the vibrational chromophore. Such simplified description of vibrational solvatochromism generally referred to as vibrational Stark effect theory has been considered to be quite appealing and, even in some cases, e.g., carbonyl stretch modes in amide, ester, ketone, and carbonate compounds or proteins, it works quantitatively well, which makes it highly useful in determining the strength of local electric field around the IR chromophore. However, noting that the vibrational frequency shift results from changes of solute-solvent intermolecular interaction potential along its normal coordinate, Pauli exclusion repulsion, polarization, charge transfer, and dispersion interactions, in addition to the electrostatic interaction between distributed charges of both vibrational chromophore and solvent molecules, are to be properly included in the theoretical description of vibrational solvatochromism. Since the electrostatic and nonelectrostatic intermolecular interaction components have distinctively different distance and orientation dependences, they affect the solvatochromic vibrational properties in a completely different manner. Over the past few years, we have developed a systematic approach to simulating vibrational solvatochromic data based on the effective fragment potential approach, one of the most accurate and rigorous theories on intermolecular interactions. We have further elucidated the interplay of local electric field with the general vibrational solvatochromism of small IR probes in either solvents or complicated biological systems, with emphasis on contributions from non-Coulombic intermolecular interactions to vibrational frequency shifts and fluctuations. With its rigorous foundation and close relation to quantitative interpretation of experimental data, this and related theoretical approaches and experiments will be of use in studying and quantifying the structure and dynamics of biomolecules with unprecedented time and spatial resolution when combined with time-resolved vibrational spectroscopy and chemically sensitive vibrational imaging techniques.

Isonitrile as an Ultrasensitive Infrared Reporter of Hydrogen-Bonding Structure and Dynamics.

Infrared (IR) probes based on terminally blocked ß-isocyanoalanine (AlaNC) and p-isocyanophenylalanine (PheNC) amino acids were synthesized. These isonitrile (NC)-derivatized compounds were extensively characterized by FTIR and femtosecond IR pump-probe spectroscopies, and a direct comparison was made with popularly used nitrile (CN)- and azide (N3)-derivatized analogs. It is shown that the isonitrile stretch frequency exhibits extremely high sensitivity to hydrogen-bonding interactions. In addition, the IR intensity of the isonitrile group is much higher than that of the nitrile group and almost as intense as that of the azido group. Furthermore, its vibrational lifetime is much longer than that of the nitrile and azido groups. To elucidate the origin of such a high H-bond sensitivity and IR intensity observed for isonitrile, extensive quantum chemical calculations were performed. It is shown that the Coulombic contributions to the vibrational frequency shifts of the isonitrile and nitrile stretch modes have opposite signs but similar magnitudes, whereas the contributions of exchange repulsion and charge delocalization to their frequency shifts are comparable. Therefore, the isonitrile stretch frequency is much more sensitive to H-bonding interactions because the blue-shifting exchange-repulsion effects are additionally enforced by such electrostatic effects. It is also shown that the much higher IR intensity of the isonitrile group compared to that of the nitrile group is due to the configuration reversal of the atomic electronegativity between the NC and CN groups. Owing to these features, we believe that isonitrile is a much better IR reporter of H-bonding structure and dynamics than the widely used nitrile and azide.

Vibrational solvatochromism of nitrile infrared probes: beyond the vibrational Stark dipole approach.

Systematic probing of local environments around biopolymers is important for understanding their functions. Therefore, there has been growing interest in in situ measurements of molecular granularity and heterogeneity through the systematic analysis of vibrational frequency shifts of carbonyl and nitrile infrared probes by vibrational Stark dipole theory. However, here we show that the nitrile vibrational frequency shift induced by its interaction with the surrounding molecules cannot be solely described by electric field-based theory because of the exchange-repulsion and dispersion interaction contributions. Considering a variety of molecular environments ranging from bulk solutions to protein environments, we explore the distinct scenarios of solute-environment contacts and their traces in vibrational frequency shifts. We believe that the present work could provide a set of clues that could be potentially used to design a rigorous theoretical model linking vibrational solvatochromism and molecular topology in complex heterogeneous environments.

Water Hydrogen-Bonding Network Structure and Dynamics at Phospholipid Multibilayer Surface: Femtosecond Mid-IR Pump-Probe Spectroscopy.

The water hydrogen-bonding network at a lipid bilayer surface is crucial to understanding membrane structures and its functional activities. With a phospholipid multibilayer mimicking a biological membrane, we study the temperature dependence of water hydrogen-bonding structure, distribution, and dynamics at a lipid multibilayer surface using femtosecond mid-IR pump-probe spectroscopy. We observe two distinguished vibrational lifetime components. The fast component (0.6 ps) is associated with water interacting with a phosphate part, whereas the slow component (1.9 ps) is with bulk-like choline-associated water. With increasing temperature, the vibrational lifetime of phosphate-associated water remains constant though its relative fraction dramatically increases. The OD stretch vibrational lifetime of choline-bound water slows down in a sigmoidal fashion with respect to temperature, indicating a noticeable change of the water environment upon the phase transition. The water structure and dynamics are thus shown to be in quantitative correlation with the structural change of liquid multibilayer upon the gel-to-liquid crystal phase transition.

Distributed Multipolar Expansion Approach to Calculation of Excitation Energy Transfer Couplings.

We propose a new approach for estimating the electrostatic part of the excitation energy transfer (EET) coupling between electronically excited chromophores based on the transition density-derived cumulative atomic multipole moments (TrCAMM). In this approach, the transition potential of a chromophore is expressed in terms of truncated distributed multipolar expansion and analytical formulas for the TrCAMMs are derived. The accuracy and computational feasibility of the proposed approach is tested against the exact Coulombic couplings, and various multipole expansion truncation schemes are analyzed. The results of preliminary calculations show that the TrCAMM approach is capable of reproducing the exact Coulombic EET couplings accurately and efficiently and is superior to other widely used schemes: the transition charges from electrostatic potential (TrESP) and the transition density cube (TDC) method.

Vibrational solvatochromism. III. Rigorous treatment of the dispersion interaction contribution.

A rigorous first principles theory of vibrational solvatochromism including the intermolecular dispersion interaction, which is based on the effective fragment potential method, is developed. The present theory is an extended version of our previous vibrational solvatochromism model that took into account the Coulomb, exchange-repulsion, and induction interactions. We show that the frequency shifts of the amide I mode of N-methylacetamide in H2O and CDCl3, when combined with molecular dynamics simulations, can be quantitatively reproduced by the theory, which indicates that the dispersion interaction contribution to the vibrational frequency shift is not always negligibly small. Nonetheless, the reason that the purely Coulombic interaction model for vibrational solvatochromism works well for describing amide I mode frequency shifts in polar solvents is because the electrostatic contribution is strong and highly sensitive to the relative orientation of surrounding solvent molecules, which is in stark contrast with polarization, dispersion, and exchange-repulsion contributions. It is believed that the theory presented and discussed here will be of great use in quantitatively describing vibrational solvatochromism and electrochromism of infrared probes in not just polar solvent environments but also in biopolymers such as proteins.

Vibrational solvatochromism. II. A first-principle theory of solvation-induced vibrational frequency shift based on effective fragment potential method.

Vibrational solvatochromism is a solvation-induced effect on fundamental vibrational frequencies of molecules in solutions. Here we present a detailed first-principle coarse-grained theory of vibrational solvatochromism, which is an extension of our previous work [B. Blasiak, H. Lee, and M. Cho, J. Chem. Phys. 139(4), 044111 (2013)] by taking into account electrostatic, exchange-repulsion, polarization, and charge-transfer interactions. By applying our theory to the model N-methylacetamide-water clusters, solute-solvent interaction-induced effects on amide I vibrational frequency are fully elucidated at Hartree-Fock level. Although the electrostatic interaction between distributed multipole moments of solute and solvent molecules plays the dominant role, the contributions from exchange repulsion and induced dipole-electric field interactions are found to be of comparable importance in short distance range, whereas the charge-transfer effect is negligible. The overall frequency shifts calculated by taking into account the contributions of electrostatics, exchange-repulsion, and polarization terms are in quantitative agreement with ab initio results obtained at the Hartree-Fock level of theory.

Vibrational solvatochromism: towards systematic approach to modeling solvation phenomena.

Vibrational solvatochromic frequency shift of IR probe is an effect of interaction between local electric field and IR probe in condensed phases. Despite prolonged efforts to develop empirical maps for vibrational frequency shifts and transition dipoles of IR probes, a systematic approach to ab initio calculation of vibrational solvatochromic charges and multipoles has not been developed. Here, we report on density functional theory (DFT) calculations of N-methylacetamide (NMA) frequency shifts using implicit and coarse-grained models. The solvatochromic infrared spectral shifts are estimated based on the distributed multipole analysis of electronic densities calculated for gas-phase equilibrium structure of NMA. Thus obtained distributed solvatochromic multipole parameters are used to calculate the amide I vibrational frequency shifts of NMA in water clusters that mimic the instantaneous configurations of the liquid water. Our results indicate that the spectral shifts are primarily electrostatic in nature and can be quantitatively reproduced using the proposed model with semi-quantitative accuracy when compared to the corresponding DFT results.

On the origins of large interaction-induced first hyperpolarizabilities in hydrogen-bonded π-electronic complexes.

In this article we elucidate the origins of interaction-induced linear and nonlinear electro-optic properties of model hydrogen-bonded π-electronic complexes. In particular we report on contributions due to various interaction energy terms to excess dipole moments (Δµ), electric dipole polarizabilities (Δα), and first hyperpolarizabilities (Δß), focusing on the latter. The analysis of intermolecular interaction-induced electric properties is performed for selected model systems including quasi-linear dimers of urea, diformamide, 4-pyridone, 4-nitroaniline, and the complex of hydrogen fluoride with nitroacetylene. The nature of intermolecular interactions as well as of the Δµ and Δα is very similar in all studied complexes. However, partitioning of Δß into physically well-defined components reveals that the origins of this term, the magnitude of which is often comparable to the hyperpolarizabilities of isolated monomers, are different in each case. Our results indicate that, even though hydrogen bonding usually diminishes the nonlinear response of interacting species, the first hyperpolarizability of complexes with the nitro group acting as a proton acceptor is substantially increased, essentially due to field-induced changes of electrostatic interactions between subsystems. However, in the remaining complexes the origins of Δß are much more involved. Even though at large intermolecular separations the origins of interaction-induced electric properties are essentially due to the field-induced electrostatic and induction interactions, in the vicinity of van der Waals minimum the overlap effects cannot be neglected since they may substantially alter the predicted excess properties or even determine their magnitude and sign. On the other hand the Δß contribution due to dispersion interactions is usually negligible. Interestingly, the values of interaction-induced first hyperpolarizability in some cases depend strongly on the intermolecular separation in the vicinity of equilibrium geometry.