Vibration-induced energy relaxation in two-level system

Energy decay in a general two-level electronic system coupled to a vibrational harmonic mode interacting with a thermal bath is studied theoretically. The model assumes a general form of the off-diagonal elements (in the electronic basis) of the vibrational-electronic interaction. The cases for constant, linear, and quadratic dependence with respect to the vibrational displacement are investigated. For short-time regime, fast oscillations corresponding to a coherent energy exchange between electrons and vibrations appear. Their frequency Ω corresponds to the energy difference (ħΩ) between electronic levels. Additionally, for the case of linear or quadratic coupling, the amplitude modulation of the oscillations with the frequency ω equal to that of vibrational motion is found.     

Dynamic electron transfers in B2H6 and Cu(PH3)2(BH4)

In order to investigate the coupling of molecular vibrations and electron distribution, dynamic electron transfers in B₂H₆ and Cu(PH₃)₂(BH₄) are lated by using a new variational method. In both molecules, the dynamic electron density near bridging hydrogen atoms decreases to form the density valley by exciting specific vibrational modes. On the other hand, in both sides of the valley density hills grow up. For these molecules, similar contour maps are given by the modes with different symmetry which have large contribution of the bridging ligands. While the dynamic electron transfer of B₂H₆ arises in symmetric form, the vibrational modes of the Cu complex gives the asymmetric redistribution of the dynamic electron density. This is attributed to the difference of the symmetry between the two molecules.     

Vibrational contributions to indirect spin-spin coupling constants calculated via variational anharmonic approaches

Zero-point vibrational contributions to indirect spin-spin coupling constants for N2, CO, HF, H2O, C2H2, and CH4 are calculated via explicitly anharmonic approaches. Thermal averages of indirect spin-spin coupling constants are calculated for the same set of molecules and for C2X4, X = H, F, Cl. Potential energy surfaces have been calculated on a grid of points and analytic representations have been obtained by a linear least-squares fit in a direct product polynomial basis. Property surfaces have been represented by a fourth-order Taylor expansion around the equilibrium geometry. The electronic structure calculations employ density functional theory, and vibrational contributions to indirect spin-spin coupling constants are calculated employing vibrational self-consistent-field and vibrational configuration-interaction methods. The performance of vibrational perturbation theory and various approximate variational calculations are discussed. Thermal averages are computed by state-specific and virtual vibrational self-consistent-field methods.     

Coupling characteristics and proton transfer mechanisms of guanine–Na monohydrate

The coupling characteristics and the proton transfer mechanisms of guanine–Na⁺ monohydrate are determined in this investigation after the implementation of the geometry optimization and the harmonic vibrational frequency calculations. There are two elementary coupling modes: the interaction of monohydrated sodium ion with two heteroatoms which form a ringed coupling, and hydrogen-bond involved coupling mode. Two potential reaction pathways, coupling mode and hydration have been taken into account, and the accurate values of binding energy are corrected for basis set superposition error (BSSE) and zero-point vibrational energy (ZPVE). Relative energies of the hydrated guanine–sodium ion complexes indicate that the ringed-coupling complexes are predominant geometries with much lower energies. Monohydrated sodium ion coupling with O6 and N7 generates the most stable geometry with a five-member cycle. Sodium ion plays an important role in the tautomerization for guanine–sodium ion complexes. This investigation indicates that the stable cation-π complexes cannot be optimized for guanine–sodium ion monohydrate. Amino-involved coupling often gives rise to a twisted four-membered cycle with unrealistic distribution of positive charge and higher energies. The rotation of amino group is likely to lead to the redistribution of the base pair hydration bonding. Effective distribution of the positive charge is an important factor in the stabilization of biological systems and binding energies for the monohydrated guanine–sodium ion complexes. The enolic coupling complex has the higher energy than the keto type due to the hindrance for the positive charge.     

Vibrational exciton delocalization precludes the use of infrared intensities as proxies for surfactant accumulation on aqueous surfaces

Surface-sensitive vibrational spectroscopy is a common tool for measuring molecular organization and intermolecular interactions at interfaces. Peak intensity ratios are typically used to extract molecular information from one-dimensional spectra but vibrational coupling between surfactant molecules can manifest as signal depletion in one-dimensional spectra. Through a combination of experiment and theory, we demonstrate the emergence of vibrational exciton delocalization in infrared reflection–absorption spectra of soluble and insoluble surfactants at the air/water interface. Vibrational coupling causes a significant decrease in peak intensities corresponding to C–F vibrational modes of perfluorooctanoic acid molecules. Vibrational excitons also form between arachidic acid surfactants within a compressed monolayer, manifesting as signal reduction of C–H stretching modes. Ionic composition of the aqueous phase impacts surfactant intermolecular distance, thereby modulating vibrational coupling strength between surfactants. Our results serve as a cautionary tale against employing alkyl and fluoroalkyl vibrational peak intensities as proxies for concentration, although such analysis is ubiquitous in interface science.

Coupling between surfactant molecules at the air/water interface bleeds intensity into a diffuse background, such that single-wavelength vibrational intensity is effectively depleted at high surface coverage.     

Approximate inclusion of four-mode couplings in vibrational coupled-cluster theory

The vibrational coupled cluster (VCC) equations are analyzed in terms of vibrational Mo?ller-Plesset perturbation theory aiming specifically at the importance of four-mode couplings. Based on this analysis, new VCC methods are derived for the calculation of anharmonic vibrational energies and vibrational spectra using vibrational coupled cluster response theory. It is shown how the effect of four-mode coupling and excitations can be efficiently and accurately described using approximations for their inclusion. Two closely related approaches are suggested. The computational scaling of the so-called VCC[3pt4F] method is not higher than the fifth power in the number of vibrational degrees of freedom when up to four-mode coupling terms are present in the Hamiltonian and only fourth order when only up to three-mode couplings are present. With a further approximation, one obtains the VCC[3pt4] model which is shown to scale with at most the fourth power in the number of vibrational degrees of freedom for Hamiltonians with both three- and four-mode coupling levels, while sharing the most important characteristics with VCC[3pt4F]. Sample calculations reported for selected tetra-atomic molecules as well as the larger dioxirane and ethylene oxide molecules support that the new models are accurate and useful.     

A mixed adiabatic—diabatic representation for the vibronic coupling problem of polyatomic molecules

A model consisting of two electronic states with different symmetries and an arbitrary number of vibrational modes which couple these states is considered. After a series of canonical transformations the hamiltonian is brought into a form suited to study effects of anharmonic and vibronic couplings. Divergences typical for non-adiabatic coupling terms are avoided.     

Hydrogen-bonded acetic acid dimers: anharmonic coupling and linear infrared spectra studied with density-functional theory

Anharmonic vibrational force field calculations provide a quantitative understanding of the width and substructure of the linear IR-absorption spectrum of the O-H stretching mode in acetic acid dimers (CH3-COOH)2 and (CD3-COOH)2. Anharmonic coupling of the high-frequency upsilon(OH) mode to fingerprint and low-frequency modes is included resulting in 11- and 9-dimensional vibrational Hamiltonians. A sixth-order force field covering up to three-body interactions is used. Force constants are calculated by fitting one-dimensional potential-energy surfaces and a finite difference procedure applying density-functional theory [Becke 3 Lee-Yang-Parr 6-311+G(d,p)]. It is demonstrated that both anharmonic coupling to low-frequency modes as well as Fermi resonance coupling with fingerprint modes are important mechanisms explaining the line shape of the O-H stretching IR-absorption band in acetic acid dimers.     

Zero-point vibrational corrections to isotropic hyperfine coupling constants in polyatomic molecules

The present work addresses isotropic hyperfine coupling constants in polyatomic systems with a particular emphasis on a largely neglected, but a posteriori significant, effect, namely zero-point vibrational corrections. Using the density functional restricted-unrestricted approach, the zero-point vibrational corrections are evaluated for the allyl radical and four of its derivatives. In addition for establishing the numerical size of the zero-point vibrational corrections to the isotropic hyperfine coupling constants, we present simple guidelines useful for identifying hydrogens for which such corrections are significant. Based on our findings, we critically re-examine the computational procedures used for the determination of hyperfine coupling constants in general as well as the practice of using experimental hyperfine coupling constants as reference data when benchmarking and optimizing exchange-correlation functionals and basis sets for such calculations.     

Excitation wavelength-dependent electron-phonon and electron-vibrational coupling in the CP29 antenna complex of green plants

Electron-phonon and electron-vibrational coupling strengths of a weakly (excitonically) coupled chlorophyll a S1-->S0 transition of the CP29 antenna complex of plant photosystem II were studied by difference fluorescence-line-narrowing spectroscopy at 4.5 K. A strong, almost linear increase of the electron-phonon coupling strength toward longer wavelengths was observed, with Huang-Rhys factors Sph increasing from 0.41+/-0.05 at 680 nm to about 0.66+/-0.07 at 688 nm. The former and latter wavelengths are located close to the peak and on the red edge of the inhomogeneous site distribution function, respectively. The experimentally obtained wavelength dependence of Sph may originate either from an alteration of the electron-phonon coupling strength by the local environment of the fluorescing chromophore and/or from the presence of two isoforms of CP29, which are characterized by different coupling strengths to the protein environment. The one-phonon profile peaks at omegam=22 cm(-1) and is described by an asymmetric function composed of a Gaussian low-energy wing and a Lorentzian high-energy tail with half-widths at half-maximum of 10+/-1 and 60+/-10 cm(-1), respectively. Thirty-nine individual vibrational modes between 90 and 1665 cm(-1) were resolved, and their Huang-Rhys factors were determined, which fall in the range between 0.0004 and 0.032. The broad feature present in the overlap region of phonon and vibrational modes at about 90 cm(-1) is characterized by S=0.048. An integral value of vibrational coupling strengths Svib=0.36+/-0.05 was determined, which is similar to that observed earlier for the trimeric LHC II complex.     

Large configuration interaction calculations of nuclear spin-spin coupling constants: III. Vibrational effects in ammonia

Large configuration interaction calculations of the proton—proton coupling constant for several geometrical configurations of the ammonia molecules are reported. The analytical expressions for the energy surface and the coupling constant as functions of two cartesian displacement coordinates are fitted to the calculated values. The potential is used for the calculation of the vibrational wavefunctions for ¹⁵NH₃ and ¹⁵ND₃ species and the vibrational averaging of the coupling constant is carried out using these functions. Though the value of the coupling constants shows a very strong geometry dependence, the vibrational corrections are found to be small. A possible correlation of the proton—proton coupling constant with an angular parameter in the NH₂ group in RNH₂ compounds is indicated.     

Analysis of bridge-mediated pathways for long-range charge transfer systems

With the density matrix decomposition scheme of the path integral method, an accurate quantitative analysis on bridge-mediated pathways in long-range charge transfer processes is presented. Unlike a donor-bridge-acceptor triad, a long-range charge transfer process with a number of bridges has additional pathways in which charges always migrate through bridges but not necessarily by incoherent nearest-neighbor hopping. By employing the density matrix decomposition and sorting the incoherent nearest-neighbor and the coherent next-nearest-neighbor hopping pathways, respective contributions to the charge transfer are evaluated quantitatively. Numerical results of two series of configurations with varying degrees of coherence within the system have found that, depending on the configuration, the contribution of the coherent pathways other than superexchange pathways is significant. In the presence of the coherence, long-range charge transfer dynamics may be dominated by the through-bridge mechanism that consists of the coherent through-bridge pathways as well as the incoherent nearest-neighbor hopping pathways.     

Vibrational spectroscopy of triacetone triperoxide (TATP): anharmonic fundamentals, overtones and combination bands

The vibrational spectrum of triacetone triperoxide (TATP) is studied by the correlation-corrected vibrational self-consistent field (CC-VSCF) method which incorporates anharmonic effects. Fundamental, overtone, and combination band frequencies are obtained by using a potential based on the PM3 method and yielding the same harmonic frequencies as DFT/cc-pVDZ calculations. Fundamentals and overtones are also studied with anharmonic single-mode (without coupling) DFT/cc-pVDZ calculations. Average deviations from experiment are similar for all methods: 2.1-2.5%. Groups of degenerate vibrations form regions of numerous combination bands with low intensity: the 5600-5800 cm(-1) region contains ca. 70 overtones and combinations of CH stretches. Anharmonic interactions are analyzed.     

DNA vibrational coupling revealed with two-dimensional infrared spectroscopy: insight into why vibrational spectroscopy is sensitive to DNA structure

Two-dimensional infrared (2D IR) spectroscopy was used to study the carbonyl vibrational modes of guanine and cytosine bases in A- and B-form DNA. Located between 1600 and 1700 cm(-1), these modes are often used to monitor DNA secondary structure with traditional infrared spectroscopies such as FTIR, but traditional spectroscopies lack the necessary observables to unravel the coupling mechanisms that make these modes sensitive to secondary structure. By using 2D IR spectroscopy and electronic structure calculations on d(G(5)C(5)) and d(GC)(8) model nucleic acids, we find that hydrogen-bonded guanine/cytosine base pairs are primarily electrostatically coupled and that the coupling between these modes can be modeled with a transition dipole density approach. In comparison, electrostatics is insufficient to model stacked bases because of cooperative charge-sharing effects, but the coupling can be accurately calculated using a finite difference method. We find that the coupling is very strong for both hydrogen-bonded and stacked base geometries, creating vibrational modes that extend both across the base pairs and along the lengths of the helices. Our results provide a physical basis for understanding how strong coupling gives rise to the empirically established relationship between infrared spectroscopy and DNA/RNA secondary structure.     

Intermolecular vibrational relaxation in liquids

The influence of intermolecular vibrational relaxation on dipole moment correlation functions, as obtained from IR band shapes, is discussed. It is explicitly shown that vibrational relaxation due to intermolecular interactions depends on the reorientational behaviour of the molecules in the liquid.Therefore, an a priori separation of the dipole moment correlation function into independent reorientational and vibrational factors is not generally possible. The implications for various procedures used to “correct” Raman and IR band shapes for vibrational relaxation are discussed.The expression derived for the intermolecular vibrational relaxation is used to calculate theoretically the effect of transition dipole-transition dipole coupling on dipole moment correlation functions.Experimental data obtained from isotopic dilution measurements support the interpretation of the isotopic dilution effect in terms of the transition dipole-transition dipole coupling.     

On the number of significant mode-mode anharmonic couplings in vibrational calculations: Correlation-corrected vibrational self-consistent field treatment of di-, tri-, and tetrapeptides

A computational study is made of the number of important anharmonic mode-mode couplings in the context of vibrational calculations for di-, tri-, and tetrapeptides. The method employed is the correlation-corrected vibrational self-consistent field (CC-VSCF) algorithm, which includes correlation effects between different vibrational modes. It is found that results of good accuracy can be obtained in calculations that include only N log N mode-mode coupling terms, where N is the number of modes. This simplification significantly accelerates CC-VSCF calculations for large molecules. A criterion based on the characteristics of the normal-mode displacements is employed to predict a priori unimportant coupling terms. The criterion is tested statistically using Spearman's rank correlation coefficient. The results are illustrated by calculations for several di-, tri-, and tetrapeptides using semiempirical PM3 potential surfaces. These results are analyzed and a statistical model for error estimation is given. The decrease in the number of included coupling from N(2) to N log N opens possibilities of anharmonic vibrational calculations for large peptides.     

Dynamics of quantum wave packets in complex molecules traced by 2D coherent electronic correlation spectroscopy

Electronic and nuclear molecular wavepackets are a clear manifestation of the wavelike properties of matter at the very heart of quantum mechanics. In this work we demonstrate how electronic two-dimensional spectroscopy (2D) serves as a highly evolved tool for the simultaneous investigation of both phenomena. In further analysis and theoretical treatments, 2D spectra form an ideal basis for the discussion of electronic decoherence, vibrational relaxation and electron-phonon coupling.     

Femtosecond primary events in bacteriorhodopsin and its retinal modified analogs: revision of commonly accepted interpretation of electronic spectra of transient intermediates in the bacteriorhodopsin photocycle

Femtosecond primary events in bacteriorhodopsin (BR) and its retinal modified analogs are discussed. Ultrafast time resolved electronic spectra of the primary intermediates induced in the BR photocycle are discussed along with spectral and kinetic inconsistencies of the previous models proposed in the literature. The theoretical model proposed in this paper based on vibrational coupling between the electronic transition of the chromophore and intramolecular vibrational modes allows us to calculate the equilibrium electronic absorption band shape and the hole burning profiles. The model is able to rationalize the complex pattern of behavior for the primary events in BR and explain the origin of the apparent inconsistencies between the experiment and the previous theoretical models. The model presented in the paper is based on the anharmonic coupling assumption in the adiabatic approximation using the canonical transformation method for diagonalization of the vibrational Hamiltonian instead of the commonly used perturbation theory. The electronic transition occurs between the Born-Oppenheimer potential energy surfaces with the electron involved in the transition being coupled to the intramolecular vibrational modes of the molecule (chromophore). The relaxation of the excited state occurs by indirect damping (dephasing) mechanisms. The indirect dephasing is governed by the time evolution of the anharmonic coupling constant driven by the resonance energy exchange between the intramolecular vibrational mode and the bath. The coupling with the intramolecular vibrational modes results in the Franck-Condon progression of bands that are broadened due to the vibrational dephasing mechanisms. The electronic absorption line shape has been calculated based on the linear response theory whereas the third order nonlinear response functions have been used to analyze the hole burning profiles obtained from the pump-probe time-resolved measurements. The theoretical treatment proposed in this paper provides a basis for a substantial revision of the commonly accepted interpretation of the primary events in the BR photocycle that exists in the literature.     

Direct identification and decongestion of Fermi resonances by control of pulse time ordering in two-dimensional IR spectroscopy

We show that it is possible to both directly measure and directly calculate Fermi resonance couplings in benzene. The measurement method used was a particular form of two-dimensional infrared spectroscopy (2D-IR) known as doubly vibrationally enhanced four wave mixing. By using different pulse orderings, vibrational cross peaks could be measured either purely at the frequencies of the base vibrational states or split by the coupling energy. This capability is a feature currently unique to this particular form of 2D-IR and can be helpful in the decongestion of complex spectra. Five cross peaks of the ring breathing mode nu13 with a range of combination bands were observed spanning a region of 1500-4550 cm(-1). The coupling energy was measured for two dominant states of the nu13+nu16 Fermi resonance tetrad. Dephasing rates were measured in the time domain for nu13 and the two (nu13+nu16) Fermi resonance states. The electronic and mechanical vibrational anharmonic coefficients were calculated to second and third orders, respectively, giving information on relative intensities of the cross peaks and enabling the Fermi resonance states of the combination band nu13+nu16 at 3050-3100 cm(-1) to be calculated. The excellent agreement between calculated and measured spectral intensities and line shapes suggests that assignment of spectral features from ab initio calculations is both viable and practicable for this form of spectroscopy.