Vibrational Delocalization Research Articles

A quasi-classical study in a quantum spirit of mode specificity of the H + HOD abstraction reaction.

Quantum benchmark calculations of the H + HOD abstraction reaction [B. Zhao et al., Phys. Chem. Chem. Phys., 2018, 20, 17029-17037] provide an opportunity to test approximate methods, such as quasi-classical trajectories (QCTs) with Gaussian binning. However, the large mode-specific enhancements of this reaction lead to special challenges and unphysical QCT cross-section artifacts. We propose and apply a general backward-forward-backward (BFB) trajectory procedure to avoid cross-section artifacts arising from vibrational motion delocalization of the initially prepared reactants. We also develop and apply a general hybrid weighting scheme, in which vibrationally adiabatic products receive unit weights, while vibrationally non-adiabatic products are Gaussian weighted. Motivated by examination of the product vibrational actions, the hybrid weighting is necessary to avoid large cross-section errors. These QCTs with Gaussian weighting extensions are general and are recommended for future polyatomic reaction simulations.

Raman spectroscopy of isotopically pure and diluted high‐ and low‐density amorphous ices

AbstractWe present an experimental and theoretical study of Raman spectroscopy of isotopically pure and diluted amorphous as well as crystalline ices at 30 K. Our experiments comprise polarized (VV) and depolarized (VH) spectra in the OH‐stretch region, whereas our calculations involve molecular dynamics (MD) simulation of the high‐ and low‐density amorphous ices through vitrification and subsequent formulation of vibrational Hamiltonian of coupled OH oscillators in the hydrogen‐bond network of the ices. Our theoretical Raman VV and VH spectra at each isotopic dilution are in good agreement with the experimental data. This allows us not only to carry out detailed spectral assignments for the amorphous and crystalline ices from the viewpoint of vibrational phase, delocalization, and density of states but also to confirm the reliability of the MD simulation in which deeply supercooled liquid water spontaneously separates into high‐ and low‐density fluid phases below a liquid–liquid critical point.

Normal mode calculation and infrared spectroscopy of proteins in water solution: Relationship between amide I transition dipole strength and secondary structure

Dipole Strength (DS) of the amides has gained a renewed interest in chemical physics since it provides an important tool to disclose the on-site vibrational energy distributions. Apart from earlier experimental efforts on polypeptides, little is still known about DS in complex proteins. We accurately measured the Fourier Transform Infrared absorption spectra of nine proteins in water solution obtaining their Molar Extinction Coefficient in the amide I and II spectral region. Our results show that the amide I DS value depends on the protein secondary structure, being that of the α-rich and unstructured proteins lower by a factor of 2 than that of the β-rich proteins. The average DS for amino acids in α and β secondary structures confirms this finding. Normal Mode calculation and Molecular Dynamics were performed and used as tools for data analysis and interpretation. The present outcomes corroborate the hypothesis that antiparallel β-sheet environment is more prone to delocalize the on-site CO stretching vibration through coupling mechanisms between carbonyl groups, whereas α-helix structures are energetically less stable to permit vibrational mode delocalization.

Exploring the anharmonic vibrational structure of carbon dioxide trimers.

Our previously developed mbCO2 potential [O. Sode and J. N. Cherry, J. Comput. Chem. 38, 2763 (2017)] is used to describe the vibrational structure of the intermolecular motions of the CO2 trimers: barrel-shaped and cyclic trimers. Anharmonic corrections are accounted for using the vibrational self-consistent field theory, vibrational second-order Møller-Plesset perturbation (VMP2) theory, and vibrational configuration interaction (VCI) methods and compared with experimental observations. For the cyclic structure, we revise the assignments of two previously observed experimental peaks based on our VCI and VMP2 results. We note that the experimental band observed near 13 cm-1 is the out-of-phase out-of-plane degenerate motion with E″ symmetry, while the peak observed at 18 cm-1 likely corresponds to the symmetric out-of-plane torsion A″ vibration. Since the VCI treatment of the vibrational motions accounts for vibrational mixing and delocalization, overtones and combination bands were also observed and quantified in the intermolecular regions of the two trimer isomers.

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.

Infrared Spectroscopy Reveals the Preferred Motif Size and Local Disorder in Parallel Stranded DNA G-Quadruplexes.

Infrared spectroscopy detects the formation of G-quadruplexes in guanine-rich nucleic acid sequences through shifts in the guanine C=O stretch mode. Here, we use ultrafast 2D infrared (IR) spectroscopy and isotope substitution to show that these shifts arise from vibrational delocalization among stacked G-quartets. This provides a direct measure of the sizes of locally ordered motifs in heterogeneous samples with substantial disordered regions. We find that parallel-stranded, potassium-bound DNA G-quadruplexes are limited to five consecutive G-quartets and 3-4 consecutive layers are preferred for longer polyguanine tracts. The resulting potassium-dependent G-quadruplex assembly landscape reflects the polyguanine tract lengths found in genomes, the ionic conditions prevalent in healthy mammalian cells, and the onset of structural disorder in disease states. Our study describes spectral markers that can be used to probe other G-quadruplex structures and provides insight into the fundamental limits of their formation in biological and artificial systems.

Vibrational Couplings in Hydridocarbonyl Complexes: A 2D-IR Perspective.

Hydridocarbonyl complexes, a class of industrially relevant catalysts, contain both the M-H and M-CO moieties. Here, using two-dimensional infrared spectroscopy, we examine the coupling of the typically weak M-H stretching mode and the intense M(C≡O) mode. By studying a series of Ir(I)- and Ir(III)-based hydridocarbonyl complexes, we show that the arrangement of the H and CO ligands in a trans configuration leads to strong vibrational coupling and mode delocalization. In contrast, a cis arrangement leads to no coupling, with the localized M-H mode having a much larger anharmonicity. These results highlight a promising strategy for enhancing the M-H vibration by intensity borrowing from the strong C≡O modes in a trans configuration, allowing for direct determination by infrared spectroscopy of both the oxidation (by frequency shifts) and the protonation state (via vibrational coupling) of the complex, in mechanistic studies of proton-coupled electron transfer reactions.

Vibrational exciton nanoimaging of phases and domains in porphyrin nanocrystals

Much of the electronic transport, photophysical, or biological functions of molecular materials emerge from intermolecular interactions and associated nanoscale structure and morphology. However, competing phases, defects, and disorder give rise to confinement and many-body localization of the associated wavefunction, disturbing the performance of the material. Here, we employ vibrational excitons as a sensitive local probe of intermolecular coupling in hyperspectral infrared scattering scanning near-field optical microscopy (IR s-SNOM) with complementary small-angle X-ray scattering to map multiscale structure from molecular coupling to long-range order. In the model organic electronic material octaethyl porphyrin ruthenium(II) carbonyl (RuOEP), we observe the evolution of competing ordered and disordered phases, in nucleation, growth, and ripening of porphyrin nanocrystals. From measurement of vibrational exciton delocalization, we identify coexistence of ordered and disordered phases in RuOEP that extend down to the molecular scale. Even when reaching a high degree of macroscopic crystallinity, identify significant local disorder with correlation lengths of only a few nanometers. This minimally invasive approach of vibrational exciton nanospectroscopy and -imaging is generally applicable to provide the molecular-level insight into photoresponse and energy transport in organic photovoltaics, electronics, or proteins.

Understanding the anharmonic vibrational structure of the carbon dioxide dimer.

Understanding the vibrational structure of the CO2 system is important to confirm the potential energy surface and interactions in such van der Waals complexes. In this work, we use our previously developed mbCO2 potential function to explore the vibrational structure of the CO2 monomer and dimer. The potential function has been trained to reproduce the potential energies at the CCSD(T)-F12b/aug-cc-pVTZ level of electronic structure theory. The harmonic approximation, as well as anharmonic corrections using vibrational structure theories such as vibrational self-consistent field, vibrational second-order Møller-Plesset perturbation, and vibrational configuration interaction (VCI), is applied to address the vibrational motions. We compare the vibrational results using the mbCO2 potential function with traditional electronic structure theory results and to experimental frequencies. The anharmonic results for the monomer most closely match the experimental data to within 3 cm-1, including the Fermi dyad frequencies. The intermolecular and intramolecular dimer frequencies were treated separately and show good agreement with the most recent theoretical and experimental results from the literature. The VCI treatment of the dimer vibrational motions accounts for vibrational mixing and delocalization, such that we observe the dimer Fermi resonance phenomena, both in the intramolecular and intermolecular regions.

Electronic energy transfer through non-adiabatic vibrational-electronic resonance. II. 1D spectra for a dimer.

Vibrational-electronic resonance in photosynthetic pigment-protein complexes invalidates Förster's adiabatic framework for interpreting spectra and energy transfer, thus complicating determination of how the surrounding protein affects pigment properties. This paper considers the combined effects of vibrational-electronic resonance and inhomogeneous variations in the electronic excitation energies of pigments at different sites on absorption, emission, circular dichroism, and hole-burning spectra for a non-degenerate homodimer. The non-degenerate homodimer has identical pigments in different sites that generate differences in electronic energies, with parameters loosely based on bacteriochlorophyll a pigments in the Fenna-Matthews-Olson antenna protein. To explain the intensity borrowing, the excited state vibrational-electronic eigenvectors are discussed in terms of the vibrational basis localized on the individual pigments, as well as the correlated/anti-correlated vibrational basis delocalized over both pigments. Compared to those in the isolated pigment, vibrational satellites for the correlated vibration have the same frequency and precisely a factor of 2 intensity reduction through vibrational delocalization in both absorption and emission. Vibrational satellites for anti-correlated vibrations have their relaxed emission intensity reduced by over a factor 2 through vibrational and excitonic delocalization. In absorption, anti-correlated vibrational satellites borrow excitonic intensity but can be broadened away by the combination of vibronic resonance and site inhomogeneity; in parallel, their vibronically resonant excitonic partners are also broadened away. These considerations are consistent with photosynthetic antenna hole-burning spectra, where sharp vibrational and excitonic satellites are absent. Vibrational-excitonic resonance barely alters the inhomogeneously broadened linear absorption, emission, and circular dichroism spectra from those for a purely electronic excitonic coupling model. Energy transfer can leave excess energy behind as vibration on the electronic ground state of the donor, allowing vibrational relaxation on the donor's ground electronic state to make energy transfer permanent by removing excess energy from the excited electronic state of the dimer.

Vibrational Characterization of Two-Dimensional Graphdiyne Sheets

Graphdiyne is formed by two acetylene bonds conjugatively connecting two phenyl rings, which then extend to a sizable two-dimensional structure. In this work, a molecular size-dependent C≡C stretching vibrational transition intensity is predicted by density functional theory in graphdiyne; in particular, the strongest infrared-active transition is enhanced in intensity by a factor of as high as 2190 from phenyl-acetylenic dimer to graphdiynic 46-mer, showing ca. 300 times enhancement per acetylene bond on average, examined at the level of B3LYP/6-31G*. Such an enhancement of vibrational transition intensity is caused by intramolecular electronic delocalization that gives rise to an enlarged transition dipole moment as well as by intramolecular vibrational delocalization that gives rise to intensity borrowing in such two-dimensionally conjugated graphdiyne molecular sheets. The enhancement is found to be diminished in defected graphdiynes. The results suggest that the periodically appearing C≡C bond may be...

The quantum structure of anionic hydrogen clusters.

A flexible and polarizable interatomic potential has been developed to model hydrogen clusters interacting with one hydrogen anion, (H2)nH-, in a broad range of sizes n = 1-54 and parametrized against coupled cluster quantum chemical calculations. Using path-integral molecular dynamics simulations at 1 K initiated from the putative classical global minima, the equilibrium structures are found to generally rely on icosahedral shells with the hydrogen molecules pointing toward the anion, producing geometric magic numbers at sizes n = 12, 32, and 44 that are in agreement with recent mass spectrometry measurements. The energetic stability of the clusters is also connected with the extent of vibrational delocalization, measured here by the fluctuations among inherent structures hidden in the vibrational wave function. As the clusters grow, the outer molecules become increasingly free to rotate, and strong finite size effects are also found between magic numbers, associated with more prominent vibrational delocalization. The effective icosahedral structure of the 44-molecule cluster is found to originate from quantum nuclear effects as well, the classical structure showing no particular symmetry.

Coating of $$\hbox {C}_{60}$$ C 60 by para- $$\hbox {H}_2$$ H 2 and ortho- $$\hbox {D}_2$$ D 2 : revisiting the solvation shell—CMMSE

The solvation of Buckminsterfullerene \(\hbox {C}_{60}\) by para-hydrogen and ortho-deuterium clusters has been modeled using a dedicated potential and path-integral molecular dynamics simulations at low temperature (2 K). The solvation shell obtained from the distribution of radial distances is found to be complete near 50 molecules, in agreement with recent mass spectrometry measurements. Deuteration increases the shell size by one, indicating a denser shell owing to less prominent vibrational delocalization for this heavier isotope.

Nuclear quantum effects on the thermal expansion coefficient of hexagonal boron nitride monolayer

This work examines the importance of vibrational delocalization on a basic thermomechanical property of a hexagonal boron nitride monolayer, namely its thermal expansion coefficient (TEC). Using a recently parametrized bond-order potential of the Tersoff type, the TEC was theoretically obtained from the thermal variations of the lattice parameter a(T) calculated using three different methods: (i) the quasiharmonic approximation; (ii) its anharmonic improvement based on self-consistent phonons; (iii) fully anharmonic Monte Carlo simulations possibly enhanced within the path-integral framework to account for nuclear quantum effects. The results obtained with the three methods are generally consistent with one another and with other recently published data, and indicate that the TEC is negative at least up to ca. 700 K, quantum mechanical effects leading to a significant expansion by about 50% relative to the classical result. Comparison with experimental data on bulk hexagonal BN suggests significant differences, which originate from possible inaccuracies in the model that tend to underestimate the lattice parameter itself, and most likely from the 2D nature of the monolayer and the key contribution of out-of-plane modes. The effects of isotopic purity in the natural abundances of boron are found to be insignificant.

Communication: Nucleation of water on ice nanograins: Size, charge, and quantum effects.

The sticking cross sections of water molecules on cold size-selected water clusters have been simulated using classical and quantum (path-integral) molecular dynamics trajectories under realistic conditions. The integrated cross sections for charged clusters show significant size effects with comparable trends as in experiments, as well as essentially no sign effect. Vibrational delocalization, although it contributes to enlarging the geometric cross sections, leads to a counter-intuitive decrease in the dynamical cross section obtained from the trajectories. These results are interpreted based on the apparent reduction in the effective interaction between the projectile and the target owing to zero-point effects.

Applicability of Quantum Thermal Baths to Complex Many-Body Systems with Various Degrees of Anharmonicity.

The semiclassical method of quantum thermal baths by colored noise thermostats has been used to simulate various atomic systems in the molecular and bulk limits, at finite temperature and in moderately to strongly anharmonic regimes. In all cases, the method performs relatively well against alternative approaches in predicting correct energetic properties, including in the presence of phase changes, provided that vibrational delocalization is not too strong-neon appearing already as an upper limiting case. In contrast, the dynamical behavior inferred from global indicators such as the root-mean-square bond length fluctuation index or the vibrational spectrum reveals more marked differences caused by zero-point energy leakage, except in the case of isolated molecules with well separated vibrational modes. To correct for such deficiencies and reduce the undesired transfer among modes, empirical modifications of the noise power spectral density were attempted to better describe thermal equilibrium but still failed when used as semiclassical preparation for microcanonical trajectories.

Coating Polycyclic Aromatic Hydrocarbon Cations with Helium Clusters: Snowballs and Slush.

The classical and quantum structures of cationic polycyclic aromatic hydrocarbon molecules (benzene, pyrene, coronene, and circumcoronene) coated by helium atoms have been theoretically investigated using a variety of computational methods. Classical shell filling, as determined from global optimization, is generally found to proceed by epitaxial additions on the graphitic surfaces before peripheral closure. From the quantum mechanical perspective provided by path-integral molecular dynamics simulations, vibrational delocalization is found to generally decrease the size of this first solvation shell, but also to give rise to a variety of situations in which the helium atoms are more or less localized depending on their environment, with strong finite size effects depending both on the hydrocarbon cation and the number of coating helium atoms. While the graphitic planes tend to bind helium sufficiently to give rise to snowball precursors, the peripheral regions are less dense and more delocalized, not as liquid as the outer layers but within an intermediate slushy character.

Theoretical investigation of the relative stability of Na⁺He(n) (n = 2-24) clusters: many-body versus delocalization effects.

The solvation of the Na(+) ion in helium clusters has been studied theoretically using optimization methods. A many-body empirical potential was developed to account for Na(+)-He and polarization interactions, and the most stable structures of Na(+)He(n) clusters were determined using the basin-hopping method. Vibrational delocalization was accounted for using zero-point energy corrections at the harmonic or anharmonic levels, the latter being evaluated from quantum Monte Carlo simulations for spinless particles. From the static perspective, many-body effects are found to play a minor role, and the structures obtained reflect homogeneous covering up to n = 10, followed by polyicosahedral packing above this size, the cluster obtained at n = 12 appearing particularly stable. The cationic impurity binds the closest helium atoms sufficiently to negate vibrational delocalization at small sizes. However, this snowball effect is obliterated earlier than shell completion, the nuclear wavefunctions of (4)He(n)Na(+) with n = 5-7, and n > 10 already exhibiting multiple inherent structures. The decrease in the snowball size due to many-body effects is consistent with recent mass spectrometry measurements.

A direct evidence of vibrationally delocalized response at ice surface.

Surface-specific vibrational spectroscopic responses at isotope diluted ice and amorphous ice are investigated by molecular dynamics (MD) simulations combined with quantum mechanics/molecular mechanics calculations. The intense response specific to the ordinary crystal ice surface is predicted to be significantly suppressed in the isotopically diluted and amorphous ices, demonstrating the vibrational delocalization at the ordinary ice surface. The collective vibration at the ice surface is also analyzed with varying temperature by the MD simulation.

New Insights on Interactions of a Quantum Vibration with an Environment of Hydrogen-Bonded Groups from the Mixed Quantum-Classical Liouville Approach

How the energy released during ATP hydrolysis can perform work in proteins despite being weak and short-lived has been a long-standing open question in biology. To address this crisis in bioenergetics, A.S. Davydov proposed a quantum mechanical model by which amide I vibrational excitations couple to alpha-helical phonon modes in such a way as to facilitate energy storage and propagation. Because of the computational expense associated with fully quantum mechanical treatments of systems with many degrees of freedom, practical simulations of the Davydov-Scott model may be realized via a mixed quantum-classical approach. We take a novel mixed quantum-classical approach to this problem by implementing two methods for solving the mixed quantum-classical Liouville equation, a surface-hopping solution and an approximate, mean-field-like solution in which the quantum subsystem is described in terms of continuous variables. The time-scale of vibrational delocalization is investigated for a one-dimensional model of a protein alpha helix. Results from the surface-hopping model suggest that population transfer between distal sites may occur in the case of an asymmetric potential, although no transfer occurs if the vibrational excitation is treated by a mean-field description.