Anharmonic Normal Modes Research Articles

Development of a universal method for vibrational analysis of the terminal alkyne C≡C stretch.

The terminal alkyne C≡C stretch has a large Raman scattering cross section in the "silent" region for biomolecules. This has led to many Raman tag and probe studies using this moiety to study biomolecular systems. A computational investigation of these systems is vital to aid in the interpretation of these results. In this work, we develop a method for computing terminal alkyne vibrational frequencies and isotropic transition polarizabilities that can easily and accurately be applied to any terminal alkyne molecule. We apply the discrete variable representation method to a localized version of the C≡C stretch normal mode. The errors of (1) vibrational localization to the terminal alkyne moiety, (2) anharmonic normal mode isolation, and (3) discretization of the Born-Oppenheimer potential energy surface are quantified and found to be generally small and cancel each other. This results in a method with low error compared to other anharmonic vibrational methods like second-order vibrational perturbation theory and to experiments. Several density functionals are tested using the method, and TPSS-D3, an inexpensive nonempirical density functional with dispersion corrections, is found to perform surprisingly well. Diffuse basis functions are found to be important for the accuracy of computed frequencies. Finally, the computation of vibrational properties like isotropic transition polarizabilities and the universality of the localized normal mode for terminal alkynes are demonstrated.

Echoes from anharmonic normal modes in model glasses.

Glasses display a wide array of nonlinear acoustic phenomena at temperatures T ≲ 1 K. This behavior has traditionally been explained by an ensemble of weakly coupled, two-level tunneling states, a theory that is also used to describe the thermodynamic properties of glasses at low temperatures. One of the most striking acoustic signatures in this regime is the existence of phonon echoes, a feature that has been associated with two-level systems with the same formalism as spin echoes in NMR. Here we report the existence of a distinctly different type of acoustic echo in classical models of glassy materials. Our simulations consist of finite-ranged, repulsive spheres and also particles with attractive forces using Lennard-Jones interactions. We show that these echoes are due to anharmonic, weakly coupled vibrational modes and perhaps provide an alternative explanation for the phonon echoes observed in glasses at low temperatures.

Infrared and Raman Spectroscopy from Ab Initio Molecular Dynamics and Static Normal Mode Analysis: The C-H Region of DMSO as a Case Study.

Carbon-hydrogen (C-H) vibration modes serve as key probes in the chemical identification of hydrocarbons and in vibrational sum-frequency generation spectroscopy of hydrocarbons at the liquid/gas interface. Their assignments pose a challenge from a theoretical viewpoint. In this work, we present a detailed study of the C-H stretching region of dimethyl sulfoxide using a new ab initio molecular dynamics (AIMD) module that we have implemented in NWChem. Through a combination of AIMD simulations and static normal mode analysis, we interpret experimental infrared and Raman spectra and explore the role of anharmonic effects in this system. Comprehensive anharmonic normal mode analysis of the C-H stretching region casts doubt upon previous experimental assignments of the shoulder on the symmetric C-H stretching peak. In addition, our AIMD simulations also show significant broadening of the in-phase symmetric C-H stretching resonance, which suggests that the experimentally observed shoulder is due to thermal broadening of the symmetric stretching resonance.

Hydrogen bonding characteristics of 2-pyrrolidinone: a joint experimental and theoretical study

The mid-IR spectrum of the hydrogen bonding lactam 2-pyrrolidinone in CCl(4) was studied using FT-IR spectroscopy accompanied by a quantum chemical anharmonic normal mode analysis combined with a Monte Carlo approach based on semi-empirical harmonic frequencies. We characterized and assigned the spectroscopic features in the range from 1500 cm(-1) to 3600 cm(-1) covering the respective amide bands related to hydrogen bonding CO and NH groups as well as the backbone CH vibrational band. By comparing theory and experiment we are able to assign all mid-IR features to a variety of distinct structures of 2-pyrrolidinone, ranging from monomers, singly and doubly hydrogen bonded dimers to longer hydrogen-bonded chains. These chains account for the most prominent features in the IR spectrum. Furthermore, two peaks in the CH band have been identified as highly localized axial and equatorial C-H stretch vibrations qualified for probes of conformational dynamics. The results provide a detailed microscopic picture of 2-pyrrolidinone in solution, helpful for further dynamical structure studies of this amide.

Finite-temperature infrared spectroscopy of polycyclic aromatic hydrocarbon molecules. II. Principal mode analysis and self-consistent phonons

Following previous work [F. Calvo et al. J. Chem. Phys. 132, 124308 (2010)], infrared spectra of several polycyclic aromatic hydrocarbon molecules are simulated with classical and quantum molecular dynamics trajectories. The interactions are modeled using a tight-binding potential energy surface and quantum delocalization is accounted for using the partially adiabatic centroid and ring-polymer molecular dynamics frameworks, both built upon the path-integral representation. The spectra obtained directly by Fourier transformation of the dipole moment autocorrelation function are here compared with several quasiharmonic approximations that provide additional information about the vibrational modes. A principal mode analysis (PMA) is carried out from the covariance matrix of atomic displacements in classical and quantum trajectories. The method systematically overestimates the line shifts due to anharmonicities, except in the power spectra of atomic displacements, and is not robust in predicting IR intensities for such large molecules. Alternatively, effective normal modes have also been determined by adapting the self-consistent phonon (SCP) theory of condensed matter physics to the present tight-binding model, in both classical and quantum mechanical descriptions. The SCP approximation turns out as semiquantitative in estimating the redshift of tight stretching modes, and performs better for classical systems. More problematic, it predicts that many low- or medium-frequency modes should be blueshifted, in contradiction with the molecular dynamics results. The sets of anharmonic normal modes extracted from the PMA and SCP approaches reveal important mixings within the tightest C-H and C-C stretching modes, which are also manifested on the corresponding power spectra.

Transferability of anharmonic force fields in simulations of molecular vibrations

Accurate simulations of vibrational molecular spectra require precise molecular force fields, at least with cubic and quartic anharmonic corrections beyond the harmonic limits. Generation of such force field terms becomes computationally prohibitive for larger molecules. In this work, an alternate possibility is explored, where approximate anharmonic force field components are obtained from molecular fragments. Transferability properties of the cubic and incomplete quartic fields are discussed and tested on model oligoproline molecules. Automatic transfer schemes including cubic, two and three atomic quartic force constants are developed and implemented. The results indicate that the main vibrational interactions in molecules are local and the anharmonic constants are mostly well amendable to the transfer. Exact anharmonic normal mode force fields of larger molecules compared very well to those obtained from smaller molecular parts. The most important changes in vibrational spectra caused by the anharmonic interactions could be reproduced with two and three atomic force field terms. The transfer scheme thus provides molecular anharmonic force fields without a significant loss of accuracy and brings significant savings of computer time and memory needed to generate molecular vibrational energies and spectra.

Anharmonic Normal Mode Analysis of Elastic Network Model Improves the Modeling of Atomic Fluctuations in Protein Crystal Structures

Protein conformational dynamics, despite its significant anharmonicity, has been widely explored by normal mode analysis (NMA) based on atomic or coarse-grained potential functions. To account for the anharmonic aspects of protein dynamics, this study proposes, and has performed, an anharmonic NMA (ANMA) based on the Cα-only elastic network models, which assume elastic interactions between pairs of residues whose Cα atoms or heavy atoms are within a cutoff distance. The key step of ANMA is to sample an anharmonic potential function along the directions of eigenvectors of the lowest normal modes to determine the mean-squared fluctuations along these directions. ANMA was evaluated based on the modeling of anisotropic displacement parameters (ADPs) from a list of 83 high-resolution protein crystal structures. Significant improvement was found in the modeling of ADPs by ANMA compared with standard NMA. Further improvement in the modeling of ADPs is attained if the interactions between a protein and its crystalline environment are taken into account. In addition, this study has determined the optimal cutoff distances for ADP modeling based on elastic network models, and these agree well with the peaks of the statistical distributions of distances between Cα atoms or heavy atoms derived from a large set of protein crystal structures.

Vibrational chaos: rational tori, separatrices and lyapunov exponents

The connections between rational tori, separatrices and Lyapunov exponents are analyzed for the model system of two anharmonic normal modes coupled by two resonances. It is shown that a clear distinction can be made between the separatrices which correspond to a fixed point and those which do not. There is no close connection between non-fixed-point separatrices and rational tori or Lyapunov exponents. In contrast fixed point separatrices are surrounded by a large number of low order rational tori of the regular system with a single resonance. Consequently, trajectories are particulary strongly distorted from an almost quasiperiodic regime around fixed point separatrices and the largest Lyapunov exponent σ 1 is proportional to the rate at which a trajectory crosses the separatrix. This leads to a well-pronounced threshold behavior for σ 1.

On the equivalence of the normal and local mode representations

The local modes Hamiltonian is rewritten exactly in terms of coupled anharmonic normal modes. Reexpressed in this way, the Hamiltonian contains leading-order 2:2 Darling–Dennison and 1:2 resonances, and terms corresponding to higher-order resonances in the highly anharmonic regime.

Coriolis-induced intramolecular vibrational energy flow between anharmonic normal modes

The classical flow of energy between anharmonic normal vibrational modes induced by Coriolis coupling is studied for a simple model of a linear triatomic molecule rotating in a plane. The dynamics are analytically solved via a mapping onto a hindered rotor representation. The theory is confirmed by trajectory calculations.

High energy vibrational states of cyanoacetylene: Variational and perturbative analysis of an anharmonic normal mode

The high energy vibrational eigenstates of cyanoacetylene are calculated with variational and perturbation theory, using a new empirical potential energy function. A detailed analysis of the eigenstates reveals that the HC bond in HCCCN is not a good local mode, even as a zeroth-order description, due predominantly to the linear geometry of the molecule. A unique anharmonic normal mode description is developed and applied to calculate accurately the eigenenergy spectrum with second-order perturbation theory. An indirect coupling scheme is presented which accounts for mixing of nearly degenerate but uncoupled high energy zeroth-order states. These results are used to account for spectral congestion in the experimental high energy spectrum of cyanoacetylene.

The high-resolution visible overtone spectrum of acetylenea)

Direct, gas-phase overtone spectra of states corresponding to five and six quanta of C–H stretch have been obtained for four isotopically substituted acetylenes in the region 14 900–18 500 cm−1. Peak positions of individual rotation–vibration lines were determined to a precision of about 0.003 cm−1. A total of 39 bands are analyzed: 16 for 12C2H2; 14 for 13C2H2; five for 12C13CH2; and four for 12C2HD. The rotational structure of the bands is fit to a semirigid rotor Hamiltonian. However, the bands suffer from severe rotational perturbations, with typical matrix elements being on the order of 0.3 cm−1 or less. The error in the determined band origins varies between 0.001 and 0.1 cm−1, depending on the degree of perturbation. Precision rotational constants are also determined for the observed bands. The vibrational term values cannot be adequately explained in terms of the usual slightly anharmonic normal mode expansion. Even though acetylene represents an intermediate case between the local mode and normal mode limits, the simple local mode theory described by Child and Lawton [M. S. Child and R. T. Lawton, Faraday Discuss. 71, 273 (1981)] can be used to rationalize many aspects of the spectrum—e.g., the splitting of the states ‖005g011〉 and ‖005u011〉 is found to be only 0.44 cm−1. The intermediate character of acetylene is seen upon single deuterium substitution. The state corresponding to five quanta of 12C–H stretch shifts about 100 cm−1 to the blue, a result which is certainly anomalous from the point of view of intuitive local mode theory. The band origins for the observed Σ–Σ transitions for all four acetylenes studied are found to be in good agreement with the results of a recent variational calculation [L. Halonen, M.S. Child, and S. Carter, Mol. Phys. 47, 1097 (1982)]. It is also observed that the anharmonic shifts of the sequence band transitions are quite large—for the v=5 overtone band, the sequence bands are shifted 74 cm−1 fo the Πg bend and 39 cm−1 for the Πu bend.

Representation of one-dimensional motion in a morse potential by a quadratic hamiltonian

A representation of the algebraic hamiltonian for the anharmonic Morse oscillator as a quadratic form, H = T1ω( 1 2 P 2 + 1 2 Q 2), where P and Q are operators is derived. The commutator of P and Q is an operator that tends to i (times the identity operator) in the harmonic limit. Coherent states and anharmonic normal modes for a linear triatomic molecule are discussed as potential applications.

A general local-mode theory for high energy polyatomic overtone spectra and application to dichloromethane

A new model is developed to describe the overtone spectra of polyatomic molecules containing XH n moieties. The infrared absorption is described as corresponding to excitation of localized modes of vibration rather than a set of symmetry allowed combinations of anharmonic normal modes. The possibility of assigning new bands in the more complex regions of the overtone spectra which involve combinations of both stretching and bending modes is examined and illustrated using the overtone spectrum of ammonia. The overtone spectrum of dichloromethane is recorded in the range λ = 9260 Å to λ = 5300 Å, and the CH overtone bands at 8850 Å, 7223 Å, and 6165 Å corresponding to the Δ v CH = 4, 5, and 6 overtones are identified. Specific features of these bands are discussed in detail in relation to the model. The common features and simplicity of the Δ v CH = 4 overtone bands of a series of halomethanes and ethanes are also interpreted in terms of the model.